diff --git a/Intersections_2/include/CGAL/Intersection_traits.h b/Intersections_2/include/CGAL/Intersection_traits.h
index adc25f0b55f..a8f75705857 100644
--- a/Intersections_2/include/CGAL/Intersection_traits.h
+++ b/Intersections_2/include/CGAL/Intersection_traits.h
@@ -23,7 +23,10 @@
 
 #include <CGAL/Kernel_traits.h>
 #include <CGAL/Object.h>
+#include <CGAL/assertions.h>
+#include <CGAL/Dimension.h>
 
+#include <boost/type_traits/is_same.hpp>
 #include <boost/variant.hpp>
 
 // The macro CGAL_INTERSECTION_VERSION controls which version of the
@@ -38,29 +41,42 @@
 #define CGAL_INTERSECTION_VERSION 2
 #endif
 
-#define CGAL_INTERSECTION_TRAITS_2(A, B, R1, R2, DIMTAG)                \
+#if CGAL_INTERSECTION_VERSION < 2
+
+#define CGAL_INTERSECTION_TRAITS_2(A, B, R1, R2)
+#define CGAL_INTERSECTION_TRAITS_3(A, B, R1, R2, R3)
+
+#else
+
+#define CGAL_INTERSECTION_TRAITS_2(A, B, R1, R2)                \
   template<typename K>     \
   struct Intersection_traits<K, typename K::A, typename K::B>  { \
     typedef typename boost::variant<typename K::R1, typename K::R2 >    \
                      variant_type;                                      \
     typedef typename boost::optional< variant_type > result_type;       \
-    typedef internal::DIMTAG Dim_tag;                                   \
   };  
 
-#define CGAL_INTERSECTION_TRAITS_3(A, B, R1, R2, R3, DIMTAG)            \
+#define CGAL_INTERSECTION_TRAITS_3(A, B, R1, R2, R3)            \
   template<typename K>     \
   struct Intersection_traits<K, typename K::A, typename K::B>  { \
     typedef typename boost::variant<typename K::R1, typename K::R2,     \
                                     typename K::R3> variant_type;       \
     typedef typename boost::optional< variant_type > result_type;       \
-    typedef internal::DIMTAG Dim_tag;                                   \
   };
 
+#endif
+
 namespace CGAL {
 
 // only declarationn
 template<typename, typename, typename>
-struct Intersection_traits {};
+struct Intersection_traits {
+  // This defaults to Object, if we use VERSION < 2 and to nothing
+  // otherwise.
+  #if CGAL_INTERSECTION_VERSION < 2
+  typedef CGAL::Object result_type;
+  #endif
+};
 
 // alias
 template<typename K, typename A, typename B>
@@ -141,61 +157,44 @@ const T* intersect_get(const boost::variant<BOOST_VARIANT_ENUM_PARAMS(U)> & v) {
   return boost::get<T>(&v);
 }
 
-// tags for dispatch
-struct Intersection_dim_two {};
-struct Intersection_dim_three {};
-struct Intersection_dim_d {};
-
 template<typename A, typename B>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT< typename CGAL::Kernel_traits<A>::Kernel, A, B>::result_type
-#endif
-intersection_impl(const A& a, const B& b, Intersection_dim_two) {
+intersection_impl(const A& a, const B& b, CGAL::Dimension_tag<2>) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().intersect_2_object()(a, b);
 }
 
 template<typename A, typename B>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT< typename CGAL::Kernel_traits<A>::Kernel, A, B>::result_type
-#endif
-intersection_impl(const A& a, const B& b, Intersection_dim_three) {
+intersection_impl(const A& a, const B& b, Dimension_tag<3>) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().intersect_3_object()(a, b);
 }
 
 template<typename A, typename B>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT< typename CGAL::Kernel_traits<A>::Kernel, A, B>::result_type
-#endif
-intersection_impl(const A& a, const B& b, Intersection_dim_d) {
+intersection_impl(const A& a, const B& b, Dynamic_dimension_tag) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().intersect_d_object()(a, b);
 }
 
 template<typename A, typename B>
 inline bool
-do_intersect_impl(const A& a, const B& b, Intersection_dim_two) {
+do_intersect_impl(const A& a, const B& b, CGAL::Dimension_tag<2>) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().do_intersect_2_object()(a, b);
 }
 
 template<typename A, typename B>
 inline bool
-do_intersect_impl(const A& a, const B& b, Intersection_dim_three) {
+do_intersect_impl(const A& a, const B& b, Dimension_tag<3>) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().do_intersect_3_object()(a, b);
 }
 
 template<typename A, typename B>
 inline bool
-do_intersect_impl(const A& a, const B& b, Intersection_dim_d) {
+do_intersect_impl(const A& a, const B& b, Dynamic_dimension_tag) {
   typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
   return Kernel().do_intersect_d_object()(a, b);
 }
@@ -204,23 +203,20 @@ do_intersect_impl(const A& a, const B& b, Intersection_dim_d) {
 
 template<typename A, typename B>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT< typename Kernel_traits<A>::Kernel, A, B>::result_type
-#endif
 intersection(const A& a, const B& b) {
-  typedef typename Kernel_traits<A>::Kernel Kernel;
-  typedef IT<Kernel, A, B> Traits;
-  return internal::intersection_impl(a, b, typename Traits::Dim_tag());
+  CGAL_static_assertion_msg( (boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value),
+                              "intersection with objects of different dimensions not supported");
+  return internal::intersection_impl(a, b, typename A::Ambient_dimension());
 }
 
 template<typename A, typename B>
-inline bool
+inline
+bool
 do_intersect(const A& a, const B& b) {
-  typedef typename Kernel_traits<A>::Kernel Kernel;
-  typedef IT<Kernel, A, B> Traits;
-  return internal::do_intersect_impl(a, b, typename Traits::Dim_tag());
+  CGAL_static_assertion_msg((boost::is_same<typename A::Ambient_dimension, typename B::Ambient_dimension>::value), 
+                        "do_intersect with objects of different dimensions not supported");
+  return internal::do_intersect_impl(a, b, typename A::Ambient_dimension());
 }
 
 } // CGAL
diff --git a/Intersections_2/include/CGAL/Intersection_traits_2.h b/Intersections_2/include/CGAL/Intersection_traits_2.h
index 8a241d42c1e..f40bf50bd37 100644
--- a/Intersections_2/include/CGAL/Intersection_traits_2.h
+++ b/Intersections_2/include/CGAL/Intersection_traits_2.h
@@ -27,31 +27,34 @@
 #include <boost/optional.hpp>
 #include <vector>
 
+#if !(CGAL_INTERSECTION_VERSION < 2)
+
 namespace CGAL {
 
-CGAL_INTERSECTION_TRAITS_2(Line_2, Line_2, Point_2, Line_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Line_2, Line_2, Point_2, Line_2)
 
-CGAL_INTERSECTION_TRAITS_2(Segment_2, Line_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Line_2, Segment_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Segment_2, Line_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Line_2, Segment_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Segment_2, Segment_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Segment_2, Segment_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Ray_2, Line_2, Point_2, Ray_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Line_2, Ray_2, Point_2, Ray_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Ray_2, Line_2, Point_2, Ray_2)
+CGAL_INTERSECTION_TRAITS_2(Line_2, Ray_2, Point_2, Ray_2)
 
-CGAL_INTERSECTION_TRAITS_2(Ray_2, Segment_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Segment_2, Ray_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Ray_2, Segment_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Segment_2, Ray_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_3(Ray_2, Ray_2, Point_2, Segment_2, Ray_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_3(Ray_2, Ray_2, Point_2, Segment_2, Ray_2)
 
-CGAL_INTERSECTION_TRAITS_2(Triangle_2, Line_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Line_2, Triangle_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Triangle_2, Line_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Line_2, Triangle_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Triangle_2, Segment_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Segment_2, Triangle_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Triangle_2, Segment_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Segment_2, Triangle_2, Point_2, Segment_2)
+
+CGAL_INTERSECTION_TRAITS_2(Triangle_2, Ray_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Ray_2, Triangle_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Triangle_2, Ray_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Ray_2, Triangle_2, Point_2, Segment_2, Intersection_dim_two)
 
 template<typename K>
 struct Intersection_traits<K, typename K::Triangle_2, typename K::Triangle_2>  {
@@ -59,17 +62,16 @@ struct Intersection_traits<K, typename K::Triangle_2, typename K::Triangle_2>  {
   boost::variant< typename K::Point_2, typename K::Segment_2,
                   typename K::Triangle_2, typename std::vector< typename K::Point_2 > > variant_type;
   typedef typename boost::optional< variant_type > result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };
 
-CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Line_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Line_2, Iso_rectangle_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Line_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Line_2, Iso_rectangle_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Segment_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Segment_2, Iso_rectangle_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Segment_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Segment_2, Iso_rectangle_2, Point_2, Segment_2)
 
-CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Ray_2, Point_2, Segment_2, Intersection_dim_two)
-CGAL_INTERSECTION_TRAITS_2(Ray_2, Iso_rectangle_2, Point_2, Segment_2, Intersection_dim_two)
+CGAL_INTERSECTION_TRAITS_2(Iso_rectangle_2, Ray_2, Point_2, Segment_2)
+CGAL_INTERSECTION_TRAITS_2(Ray_2, Iso_rectangle_2, Point_2, Segment_2)
 
 // undocumented
 
@@ -78,21 +80,18 @@ template<typename K>
 struct Intersection_traits<K, typename K::Iso_rectangle_2, typename K::Iso_rectangle_2>  {
   typedef typename boost::variant<typename K::Iso_rectangle_2> variant_type;
   typedef boost::optional<variant_type> result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };
 
 template<typename K, typename B>
 struct Intersection_traits<K, typename K::Point_2, B> {
   typedef typename boost::variant<typename K::Point_2> variant_type;
   typedef boost::optional<variant_type> result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };
 
 template<typename K, typename A>
 struct Intersection_traits<K, A, typename K::Point_2> {
   typedef typename boost::variant<typename K::Point_2> variant_type;
   typedef boost::optional<variant_type> result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };
 
 template<typename K>
@@ -102,7 +101,6 @@ struct Intersection_traits<K, typename K::Iso_rectangle_2, typename K::Triangle_
                                   typename K::Point_2, 
                                   typename std::vector< typename K::Point_2 > > variant_type;
   typedef typename boost::optional < variant_type > result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -119,7 +117,6 @@ struct Intersection_traits<K, typename K::Circle_2, typename K::Circle_2>
                   typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 
@@ -131,7 +128,6 @@ struct Intersection_traits<K, typename K::Circular_arc_2, typename K::Circular_a
                   typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -142,7 +138,6 @@ struct Intersection_traits<K, typename K::Line_arc_2, typename K::Line_arc_2>
                   typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -152,7 +147,6 @@ struct Intersection_traits<K, typename K::Line_arc_2, typename K::Circle_2>
   boost::variant< typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -167,7 +161,6 @@ struct Intersection_traits<K, typename K::Line_arc_2, typename K::Circular_arc_2
   boost::variant< typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -183,7 +176,6 @@ struct Intersection_traits<K, typename K::Line_arc_2, typename K::Line_2>
                   typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -198,7 +190,6 @@ struct Intersection_traits<K, typename K::Line_2, typename K::Circular_arc_2>
   boost::variant< typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -228,7 +219,6 @@ struct Intersection_traits<K, typename K::Line_2, typename K::Circle_2>
   boost::variant< typename std::pair< typename K::Circular_arc_point_2, 
                                       unsigned int > > 
   result_type;
-  typedef internal::Intersection_dim_two Dim_tag;
 };  
 
 template<typename K>
@@ -236,8 +226,9 @@ struct Intersection_traits<K, typename K::Circle_2, typename K::Line_2> :
     public Intersection_traits<K, typename K::Line_2, typename K::Circle_2>
 {};
 
-
 } // namespace CGAL
 
+#endif
+
 #endif /* CGAL_INTERSECTION_TRAITS_2_H */
 
diff --git a/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h b/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
index d5ae633b1af..1106af18e4c 100644
--- a/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
+++ b/Intersections_2/include/CGAL/Intersections_2/Triangle_2_Triangle_2_intersection_impl.h
@@ -318,12 +318,8 @@ Triangle_2_Triangle_2_pair<K>::intersection_point() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Triangle_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Triangle_2 &tr1, 
 	     const typename K::Triangle_2 &tr2,
 	     const K&)
diff --git a/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
index ba0864dac53..215e71fa0c7 100644
--- a/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Iso_rectangle_2_Iso_rectangle_2_intersection.h
@@ -33,12 +33,8 @@ namespace CGAL {
 namespace internal {
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Iso_rectangle_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(
     const typename K::Iso_rectangle_2 &irect1,
     const typename K::Iso_rectangle_2 &irect2,
diff --git a/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
index 9efeb3e1272..d11d63ddeb3 100644
--- a/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Iso_rectangle_2_intersection.h
@@ -184,12 +184,8 @@ intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line, 
 	     const typename K::Iso_rectangle_2 &iso,
 	     const K&)
@@ -209,12 +205,8 @@ intersection(const typename K::Line_2 &line,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Iso_rectangle_2 &iso,
 	     const typename K::Line_2 &line, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
index df463363eb1..978ffa6633c 100644
--- a/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Line_2_intersection.h
@@ -70,12 +70,8 @@ inline bool do_intersect(
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Line_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line1, 
 	     const typename K::Line_2 &line2,
 	     const K&)
diff --git a/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
index 19401ecd757..fb8b9b4bff5 100644
--- a/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Line_2_Triangle_2_intersection.h
@@ -160,12 +160,8 @@ intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line, 
 	     const typename K::Triangle_2 &tr,
 	     const K&)
@@ -186,12 +182,8 @@ intersection(const typename K::Line_2 &line,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Triangle_2 &tr,
 	     const typename K::Line_2 &line,
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
index 9ba422ae869..bf74b2205d6 100644
--- a/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Iso_rectangle_2_intersection.h
@@ -54,12 +54,8 @@ do_intersect(const typename K::Iso_rectangle_2 &iso,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Point_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Point_2 &pt,
 	     const typename K::Iso_rectangle_2 &iso,
 	     const K& k)
@@ -74,12 +70,8 @@ intersection(const typename K::Point_2 &pt,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Point_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Iso_rectangle_2 &iso,
 	     const typename K::Point_2 &pt,
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
index a06dfcd89c4..20d3391b939 100644
--- a/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Line_2_intersection.h
@@ -52,12 +52,8 @@ do_intersect(const typename K::Line_2 &line,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Point_2, typename K::Line_2>::result_type
-#endif
 intersection(const typename K::Point_2 &pt, 
 	     const typename K::Line_2 &line,
 	     const K& k)
@@ -69,12 +65,8 @@ intersection(const typename K::Point_2 &pt,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Point_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line,
 	     const typename K::Point_2 &pt, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
index b289c7183e4..7c6b52b8eff 100644
--- a/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Point_2_intersection.h
@@ -46,13 +46,10 @@ typename CGAL::Intersection_traits
 intersection(const typename K::Point_2 &pt1, 
 	     const typename K::Point_2 &pt2)
 {
-  typedef typename CGAL::Intersection_traits
-    <K, typename K::Point_2, typename K::Point_2>::result_type result_type;
-
     if (pt1 == pt2) {
-      return result_type(pt1);
+      return intersection_return<K, typename K::Point_2, typename K::Point_2>(pt1);
     }
-    return result_type();
+    return intersection_return<K, typename K::Point_2, typename K::Point_2>();
 }
 
 }// namespace internal
diff --git a/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
index 89dd34ee300..c2387e320e5 100644
--- a/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Ray_2_intersection.h
@@ -56,12 +56,8 @@ do_intersect(const typename K::Ray_2 &ray,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Point_2, typename K::Ray_2>::result_type
-#endif
 intersection(const typename K::Point_2 &pt, 
 	     const typename K::Ray_2 &ray,
 	     const K& k)
@@ -73,12 +69,8 @@ intersection(const typename K::Point_2 &pt,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Point_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray,
 	     const typename K::Point_2 &pt, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
index 41da44a0a1d..92d760f8e68 100644
--- a/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Segment_2_intersection.h
@@ -56,12 +56,8 @@ do_intersect(const typename K::Segment_2 &seg,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Point_2, typename K::Segment_2>::result_type
-#endif
 intersection(const typename K::Point_2 &pt, 
 	     const typename K::Segment_2 &seg, 
 	     const K& k)
@@ -74,12 +70,8 @@ intersection(const typename K::Point_2 &pt,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Point_2>::result_type
-#endif
 intersection( const typename K::Segment_2 &seg, 
 	      const typename K::Point_2 &pt, 
 	      const K& k)
diff --git a/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
index aa495702b9d..551b8d15a04 100644
--- a/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Point_2_Triangle_2_intersection.h
@@ -127,12 +127,8 @@ intersection_point() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Point_2, typename K::Triangle_2>
 ::result_type
-#endif
 intersection(const typename K::Point_2 &pt, 
 	     const typename K::Triangle_2 &tr,
 	     const K&)
@@ -150,12 +146,8 @@ intersection(const typename K::Point_2 &pt,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Point_2, typename K::Triangle_2>
 ::result_type
-#endif
 intersection(const typename K::Triangle_2 &tr,
 	     const typename K::Point_2 &pt, 
 	     const K&k)
diff --git a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
index af6c0bbe13e..6cc3d4ca59e 100644
--- a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
@@ -79,12 +79,8 @@ inline bool do_intersect(const typename K::Iso_rectangle_2 &p2,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray,
 	     const typename K::Iso_rectangle_2 &iso,
 	     const K& )
@@ -103,12 +99,8 @@ intersection(const typename K::Ray_2 &ray,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Iso_rectangle_2 &iso,
 	     const typename K::Ray_2 &ray,
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
index 99d19f56017..b725c949f76 100644
--- a/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Line_2_intersection.h
@@ -71,12 +71,8 @@ inline bool do_intersect(
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits
 <K, typename K::Ray_2, typename K::Line_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray,
 	     const typename K::Line_2 &line,
 	     const K&)
@@ -97,12 +93,8 @@ intersection(const typename K::Ray_2 &ray,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits
 <K, typename K::Line_2, typename K::Ray_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line,
 	     const typename K::Ray_2 &ray,
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
index 3d6314acdd4..a1264ca1bec 100644
--- a/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h
@@ -233,12 +233,8 @@ Ray_2_Ray_2_pair<K>::intersection_ray() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
   <K, typename K::Ray_2, typename K::Ray_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray1, 
 	     const typename K::Ray_2 &ray2,
 	     const K&)
diff --git a/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
index ae2421c3e31..72a9ed3994b 100644
--- a/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Segment_2_intersection.h
@@ -236,12 +236,8 @@ Ray_2_Segment_2_pair<K>::intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Segment_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray, 
 	     const typename K::Segment_2 &seg,
 	     const K&)
@@ -261,12 +257,8 @@ intersection(const typename K::Ray_2 &ray,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Segment_2>::result_type
-#endif
 intersection(const typename K::Segment_2 &seg,
 	     const typename K::Ray_2 &ray, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
index 6ae685c5154..ca2f976f06e 100644
--- a/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Triangle_2_intersection.h
@@ -142,12 +142,8 @@ intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Ray_2 &ray, 
 	     const typename K::Triangle_2&tr,
 	     const K&)
@@ -167,12 +163,8 @@ intersection(const typename K::Ray_2 &ray,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Ray_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Triangle_2&tr,
 	     const typename K::Ray_2 &ray, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
index 97b8ea37f3d..5858983167c 100644
--- a/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Iso_rectangle_2_intersection.h
@@ -74,12 +74,8 @@ inline bool do_intersect(
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(
     const typename K::Segment_2 &seg,
     const typename K::Iso_rectangle_2 &iso,
@@ -100,12 +96,8 @@ intersection(
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Iso_rectangle_2>::result_type
-#endif
 intersection(const typename K::Iso_rectangle_2 &iso,
 	     const typename K::Segment_2 &seg,
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
index b0070125eff..ad06e8223f6 100644
--- a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
@@ -69,12 +69,8 @@ inline bool do_intersect(
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Line_2>::result_type
-#endif
 intersection(const typename K::Segment_2 &seg, 
 	     const typename K::Line_2 &line,
 	     const K&)
@@ -94,12 +90,8 @@ intersection(const typename K::Segment_2 &seg,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Line_2, typename K::Segment_2>::result_type
-#endif
 intersection(const typename K::Line_2 &line,
 	     const typename K::Segment_2 &seg, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
index 812d72f44ed..4d702d217a0 100644
--- a/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Segment_2_intersection.h
@@ -431,12 +431,8 @@ Segment_2_Segment_2_pair<K>::intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Segment_2>::result_type
-#endif
 intersection(const typename K::Segment_2 &seg1, 
 	     const typename K::Segment_2 &seg2,
 	     const K&)
diff --git a/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
index efc81c3ba90..e8fdb8795b2 100644
--- a/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Triangle_2_intersection.h
@@ -153,12 +153,8 @@ intersection_segment() const
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Segment_2 &seg, 
 	     const typename K::Triangle_2&tr,
 	     const K&)
@@ -178,12 +174,8 @@ intersection(const typename K::Segment_2 &seg,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits
 <K, typename K::Segment_2, typename K::Triangle_2>::result_type
-#endif
 intersection(const typename K::Triangle_2&tr,
 	     const typename K::Segment_2 &seg, 
 	     const K& k)
diff --git a/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
index 635b6bcd236..779e13c1bb8 100644
--- a/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Triangle_2_Iso_rectangle_2_intersection.h
@@ -34,11 +34,7 @@
 namespace CGAL{
 namespace internal {
   template <class R>
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
-  typename Intersection_traits<R, typename R::Triangle_2, typename R::Iso_rectangle_2>::result_type
-  #endif
+    typename Intersection_traits<R, typename R::Triangle_2, typename R::Iso_rectangle_2>::result_type
   intersection(const Triangle_2<R> &t, const Iso_rectangle_2<R> &r, const R& rr)
   {
     typedef typename R::FT FT;
@@ -152,18 +148,10 @@ namespace internal {
               if(position[next][j]) // if it's a second point direction
               {
                 //test for intersection
-                #if CGAL_INTERSECTION_VERSION < 2
-                CGAL::Object
-                #else
                 typename Intersection_traits<R, Segment, Segment>::result_type
-                #endif                                
                   v = internal::intersection(Segment(p[index], p[next]), s[j], rr);
                 if(v) {
-                  #if CGAL_INTERSECTION_VERSION < 2
-                  if(const Point *p_obj = object_cast<Point>(v))
-                  #else
-                  if(const Point *p_obj = boost::get<Point>(&*v))
-                  #endif
+                  if(const Point *p_obj = intersect_get<Point>(v))
                   {
                     //intersection found
                     outside = true;
@@ -180,18 +168,10 @@ namespace internal {
             if(position[index][j]) //watch only the first point directions
             {
               //test for intersection
-              #if CGAL_INTERSECTION_VERSION < 2
-              CGAL::Object
-              #else
               typename Intersection_traits<R, Segment, Segment>::result_type
-              #endif
                 v = internal::intersection(Segment(p[index], p[next]), s[j], rr);
               if(v) {
-                #if CGAL_INTERSECTION_VERSION < 2
-                if(const Point *p_obj = object_cast<Point>(v))
-                #else
-                if(const Point *p_obj = boost::get<Point>(&*v))
-                #endif
+                if(const Point *p_obj = intersect_get<Point>(v))
                 {
                   //intersection found
                   outside = false;
@@ -224,19 +204,11 @@ namespace internal {
                       if(position[next][j])
                       {
                         //test for intersection
-                        #if CGAL_INTERSECTION_VERSION < 2
-                        CGAL::Object
-                        #else
                         typename Intersection_traits<R, Segment, Segment>
                           ::result_type
-                        #endif 
                           v = internal::intersection(Segment(p[index], p[next]), s[j]);
                         if(v) {
-                          #if CGAL_INTERSECTION_VERSION < 3
-                          if(const Point *p_obj = object_cast<Point>(&*v))
-                          #else
-                          if(const Point *p_obj = boost::get<Point>(&*v))
-                          #endif
+                          if(const Point *p_obj = intersect_get<Point>(v))
                             //found the second intersection
                           {
                             outside = true;
diff --git a/Intersections_3/include/CGAL/Intersection_traits_3.h b/Intersections_3/include/CGAL/Intersection_traits_3.h
index 79dc98c1691..7c7a7a4b080 100644
--- a/Intersections_3/include/CGAL/Intersection_traits_3.h
+++ b/Intersections_3/include/CGAL/Intersection_traits_3.h
@@ -24,50 +24,52 @@
 #include <CGAL/Intersection_traits.h>
 #include <CGAL/Bbox_3.h>
 
+#if !(CGAL_INTERSECTION_VERSION < 2)
+
 namespace CGAL  {
 
-CGAL_INTERSECTION_TRAITS_2(Line_3, Line_3, Point_3, Line_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Line_3, Point_3, Line_3)
 
-CGAL_INTERSECTION_TRAITS_2(Line_3, Plane_3, Point_3, Line_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Plane_3, Line_3, Point_3, Line_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Plane_3, Point_3, Line_3)
+CGAL_INTERSECTION_TRAITS_2(Plane_3, Line_3, Point_3, Line_3)
 
-CGAL_INTERSECTION_TRAITS_2(Line_3, Ray_3, Point_3, Ray_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Ray_3, Line_3, Point_3, Ray_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Ray_3, Point_3, Ray_3)
+CGAL_INTERSECTION_TRAITS_2(Ray_3, Line_3, Point_3, Ray_3)
 
-CGAL_INTERSECTION_TRAITS_2(Line_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Line_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Segment_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Line_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Line_3, Triangle_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Triangle_3, Line_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Triangle_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Triangle_3, Line_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Plane_3, Plane_3, Line_3, Plane_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Plane_3, Plane_3, Line_3, Plane_3)
 
-CGAL_INTERSECTION_TRAITS_2(Plane_3, Ray_3, Point_3, Ray_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Ray_3, Plane_3, Point_3, Ray_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Plane_3, Ray_3, Point_3, Ray_3)
+CGAL_INTERSECTION_TRAITS_2(Ray_3, Plane_3, Point_3, Ray_3)
 
-CGAL_INTERSECTION_TRAITS_2(Plane_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Plane_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Plane_3, Segment_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Plane_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Plane_3, Sphere_3, Point_3, Circle_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Sphere_3, Plane_3, Point_3, Circle_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Plane_3, Sphere_3, Point_3, Circle_3)
+CGAL_INTERSECTION_TRAITS_2(Sphere_3, Plane_3, Point_3, Circle_3)
 
-CGAL_INTERSECTION_TRAITS_3(Plane_3, Triangle_3, Point_3, Segment_3, Triangle_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_3(Triangle_3, Plane_3, Point_3, Segment_3, Triangle_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_3(Plane_3, Triangle_3, Point_3, Segment_3, Triangle_3)
+CGAL_INTERSECTION_TRAITS_3(Triangle_3, Plane_3, Point_3, Segment_3, Triangle_3)
 
-CGAL_INTERSECTION_TRAITS_3(Ray_3, Ray_3, Point_3, Ray_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_3(Ray_3, Ray_3, Point_3, Ray_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Ray_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Ray_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Ray_3, Segment_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Ray_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Ray_3, Triangle_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Triangle_3, Ray_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Ray_3, Triangle_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Triangle_3, Ray_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Segment_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Triangle_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Triangle_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Triangle_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Triangle_3, Segment_3, Point_3, Segment_3)
 
-CGAL_INTERSECTION_TRAITS_3(Sphere_3, Sphere_3, Point_3, Circle_3, Sphere_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_3(Sphere_3, Sphere_3, Point_3, Circle_3, Sphere_3)
 
 template<typename K>
 struct Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>  {
@@ -75,22 +77,21 @@ struct Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>  {
   boost::variant< typename K::Point_3, typename K::Segment_3, typename K::Triangle_3,
                   typename std::vector< typename K::Point_3 > > variant_type;
   typedef typename boost::optional< variant_type > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 // !!! undocumented !!!
 
 // Segment_3 Iso_cuboid_3
-CGAL_INTERSECTION_TRAITS_2(Segment_3, Iso_cuboid_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Segment_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Segment_3, Iso_cuboid_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Segment_3, Point_3, Segment_3)
 
 // Line_3 Iso_cuboid_3
-CGAL_INTERSECTION_TRAITS_2(Line_3, Iso_cuboid_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Line_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Line_3, Iso_cuboid_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Line_3, Point_3, Segment_3)
 
 // Ray_3 Iso_cuboid_3
-CGAL_INTERSECTION_TRAITS_2(Ray_3, Iso_cuboid_3, Point_3, Segment_3, Intersection_dim_three)
-CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Ray_3, Point_3, Segment_3, Intersection_dim_three)
+CGAL_INTERSECTION_TRAITS_2(Ray_3, Iso_cuboid_3, Point_3, Segment_3)
+CGAL_INTERSECTION_TRAITS_2(Iso_cuboid_3, Ray_3, Point_3, Segment_3)
 
 // Iso_cuboid_3 Iso_cuboid_3, variant of one
 template<typename K>
@@ -98,7 +99,6 @@ struct Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Iso_cuboid_3
   typedef typename 
   boost::variant< typename K::Iso_cuboid_3 > variant_type;
   typedef typename boost::optional< variant_type > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 // Intersections with BBox returns the same for Ray_3, Line_3 and Segment_3
@@ -108,7 +108,6 @@ struct Intersection_traits<K, CGAL::Bbox_3, typename K::Line_3>  {
   typedef typename 
   boost::variant< typename K::Segment_3, typename K::Point_3 > variant_type;
   typedef typename boost::optional< variant_type > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 template<typename K>
@@ -151,7 +150,6 @@ struct Intersection_traits<K, typename K::Circle_3, typename K::Plane_3> {
   typedef typename boost::variant< std::pair< typename K::Circular_arc_point_3,
                                               unsigned int >,
                                    typename K::Circle_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 template<typename K>
@@ -164,7 +162,6 @@ struct Intersection_traits<K, typename K::Circle_3, typename K::Sphere_3> {
   typedef typename boost::variant< std::pair< typename K::Circular_arc_point_3,
                                               unsigned int >,
                                    typename K::Circle_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 template<typename K>
@@ -176,7 +173,6 @@ template<typename K>
 struct Intersection_traits<K, typename K::Circle_3, typename K::Circle_3> {
   typedef typename boost::variant< std::pair <typename K::Circular_arc_point_3, unsigned int >, 
                                    typename K::Circle_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 // Circle_3 Circle_3
@@ -184,7 +180,6 @@ template<typename K>
 struct Intersection_traits<K, typename K::Circle_3, typename K::Line_3> {
   typedef typename boost::variant< 
     std::pair <typename K::Circular_arc_point_3, unsigned int > > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 template<typename K>
@@ -198,7 +193,6 @@ struct Intersection_traits<K, typename K::Circular_arc_3, typename K::Circular_a
     typename K::Circle_3,
     std::pair <typename K::Circular_arc_point_3, unsigned int >,
     typename K::Circular_arc_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 // Circular_arc_3 Plane_3 
@@ -207,7 +201,6 @@ struct Intersection_traits<K, typename K::Circular_arc_3, typename K::Plane_3> {
   typedef typename boost::variant< 
     std::pair <typename K::Circular_arc_point_3, unsigned int >,
     typename K::Circular_arc_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 template<typename K>
@@ -220,11 +213,12 @@ struct Intersection_traits<K, typename K::Line_arc_3, typename K::Line_arc_3> {
   typedef typename boost::variant< 
     std::pair <typename K::Circular_arc_point_3, unsigned int >,
     typename K::Line_arc_3 > result_type;
-  typedef internal::Intersection_dim_three Dim_tag;
 };
 
 
 } // namespace
 
+#endif // !(CGAL_INTERSECTION_VERSION < 2)
+
 #endif /* CGAL_INTERSECTION_TRAITS_3_H */
 
diff --git a/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h b/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
index 855b4e22fa8..8d0f5026eda 100644
--- a/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
+++ b/Intersections_3/include/CGAL/Intersections_3/intersection_3_1_impl.h
@@ -26,17 +26,14 @@
 
 #include <CGAL/wmult.h>
 #include <boost/next_prior.hpp>
+#include <CGAL/Intersection_traits_3.h>
 
 namespace CGAL {
 
 namespace internal {
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type
-#endif
 intersection(const typename K::Plane_3  &plane, 
 	     const typename K::Line_3 &line, 
 	     const K&)
@@ -70,11 +67,7 @@ intersection(const typename K::Plane_3  &plane,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type
-#endif
 intersection(const typename K::Line_3 &line, 
 	     const typename K::Plane_3  &plane, 
 	     const K& k)
@@ -83,11 +76,7 @@ intersection(const typename K::Line_3 &line,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Plane_3>::result_type
-#endif
 intersection(const typename K::Plane_3 &plane1, 
 	     const typename K::Plane_3 &plane2, 
 	     const K&)
@@ -159,10 +148,16 @@ intersection(const typename K::Plane_3 &plane1,
 	     const typename K::Plane_3 &plane3,
 	     const K& k)
 {
-    typedef typename boost::optional< 
+    typedef 
+      #if CGAL_INTERSECTION_VERSION < 2
+      CGAL::Object
+      #else
+      typename boost::optional< 
       boost::variant<typename K::Point_3,
                      typename K::Line_3,
-                     typename K::Plane_3> > result_type;
+                     typename K::Plane_3> > 
+      #endif
+      result_type;
 
 
     typedef typename K::Point_3      Point_3;
@@ -171,61 +166,45 @@ intersection(const typename K::Plane_3 &plane1,
 
     // Intersection between plane1 and plane2 can either be
     // a line, a plane, or empty.
-    #if CGAL_INTERSECTION_VERSION < 2
-    CGAL::Object
-    #else
     typename Intersection_traits<K, Plane_3, Plane_3>::result_type
-    #endif
       o12 = internal::intersection(plane1, plane2, k);
     
     if(o12) {
       if(const Line_3* l = intersect_get<Line_3>(o12)) {
         // either point or line
-        #if CGAL_INTERSECTION_VERSION < 2
-        CGAL::Object
-        #else
         typename Intersection_traits<K, Plane_3, Line_3>::result_type 
-        #endif
           v = internal::intersection(plane3, *l, k);
         if(v) {
-          // don't use intersect get, we don't have traits and can't
-          // use intersect_return.
-          #if CGAL_INTERSECTION_VERSION < 2
-          if(const Point_3* p = object_cast<Point_3>(&v))
+          if(const Point_3* p = intersect_get<Point_3>(v))
+            #if CGAL_INTERSECTION_VERSION < 2
             return make_object(*p);
-          else if(const Line_3* l = object_cast<Line_3>(&v))
-            return make_object(*l);
-          #else
-          if(const Point_3* p = boost::get<Point_3>(&*v))
+            #else
             return result_type(*p);
-          else if(const Line_3* l = boost::get<Line_3>(&*v))
+            #endif
+          else if(const Line_3* l = intersect_get<Line_3>(v))
+            #if CGAL_INTERSECTION_VERSION < 2
+            return make_object(*l);
+            #else
             return result_type(*l);
-          #endif
+            #endif
         }
-      #if CGAL_INTERSECTION_VERSION < 2
-      } else if(const Plane_3 *pl = object_cast<Plane_3>(&o12)) {
-      #else
-      } else if(const Plane_3 *pl = boost::get<Plane_3>(&(*o12))) {
-      #endif
+      } else if(const Plane_3 *pl = intersect_get<Plane_3>(o12)) {
         // either line or plane
-        #if CGAL_INTERSECTION_VERSION < 2
-        CGAL::Object
-        #else
         typename Intersection_traits<K, Plane_3, Plane_3>::result_type 
-        #endif
           v = internal::intersection(plane3, *pl, k);
         if(v) {
-          #if CGAL_INTERSECTION_VERSION < 2
-          if(const Plane_3* p = object_cast<Plane_3>(&v))
+          if(const Plane_3* p = intersect_get<Plane_3>(v))
+            #if CGAL_INTERSECTION_VERSION < 2
             return make_object(*p);
-          else if(const Line_3* l = object_cast<Line_3>(&v))
-            return make_object(*l);
-          #else
-          if(const Plane_3* p = boost::get<Plane_3>(&*v))
+            #else
             return result_type(*p);
-          else if(const Line_3* l = boost::get<Line_3>(&*v))
+            #endif
+          else if(const Line_3* l = intersect_get<Line_3>(v))
+            #if CGAL_INTERSECTION_VERSION < 2
+            return make_object(*l);
+            #else
             return result_type(*l);
-          #endif
+            #endif
         }
       }
     }
@@ -276,11 +255,7 @@ do_intersect(const typename K::Line_3 &line,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, typename K::Line_3>::result_type
-#endif
 intersection(const typename K::Line_3 &l1,
 	     const typename K::Line_3 &l2,
 	     const K&)
@@ -338,11 +313,7 @@ do_intersect(const typename K::Line_3 &l1,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Segment_3>::result_type
-#endif
 intersection_collinear_segments(const typename K::Segment_3 &s1,
                                 const typename K::Segment_3 &s2,
                                 const K& k)
@@ -381,13 +352,9 @@ intersection_collinear_segments(const typename K::Segment_3 &s1,
 
 template<class K>
 struct L_p_visitor : public boost::static_visitor< 
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
   typename Intersection_traits<K, typename K::Segment_3, 
-                                 typename K::Segment_3>::result_type
-#endif 
-> 
+                               typename K::Segment_3>::result_type
+  > 
 {
 
   typedef typename Intersection_traits<K, typename K::Segment_3, 
@@ -397,46 +364,30 @@ CGAL::Object
   const typename K::Segment_3& s1;
   const typename K::Segment_3& s2;
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   result_type
-  #endif
   operator()(const typename K::Point_3& p) const {
     typename K::Collinear_are_ordered_along_line_3 cln_order=K().collinear_are_ordered_along_line_3_object();
     if ( cln_order(s1[0],p,s1[1]) && cln_order(s2[0],p,s2[1]) )
-      return result_type(p);
+      return intersection_return<K, typename K::Segment_3, typename K::Segment_3>(p);
     else
-      return result_type();
+      return intersection_return<K, typename K::Segment_3, typename K::Segment_3>();
   }
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   result_type
-  #endif
   operator()(const typename K::Line_3&) const {
     return intersection_collinear_segments(s1,s2,K());
   }
 };
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &s1,
 	     const typename K::Segment_3 &s2,
 	     const K&)
 {
   CGAL_precondition(! s1.is_degenerate () && ! s2.is_degenerate () );
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Line_3, typename K::Line_3>::result_type 
-  #endif
     v = internal::intersection(s1.supporting_line(),s2.supporting_line(), K());
 
   if(v) {
@@ -488,22 +439,14 @@ do_intersect(const typename K::Segment_3  &s1,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Line_3 &l,
 	     const typename K::Segment_3 &s,
 	     const K& k)
 {
   CGAL_precondition(! l.is_degenerate () && ! s.is_degenerate () );
   
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else 
   typename Intersection_traits<K, typename K::Line_3, typename K::Line_3>::result_type 
-  #endif
     v = internal::intersection(l,s.supporting_line(), K());
 
   if(v) {
@@ -520,11 +463,7 @@ intersection(const typename K::Line_3 &l,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &s,
 	     const typename K::Line_3 &l,
 	     const K& k)
@@ -584,22 +523,14 @@ Ray_3_has_on_collinear_Point_3(
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Line_3 &l,
 	     const typename K::Ray_3 &r,
 	     const K& k)
 {
   CGAL_precondition(! l.is_degenerate () && ! r.is_degenerate () );
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else 
   typename Intersection_traits<K, typename K::Line_3, typename K::Line_3>::result_type 
-  #endif
     v = internal::intersection(l,r.supporting_line(), k);
   
   if(v) {
@@ -614,11 +545,7 @@ intersection(const typename K::Line_3 &l,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Line_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &r,
 	     const typename K::Line_3 &l,
 	     const K& k)
@@ -655,22 +582,14 @@ do_intersect(const typename K::Ray_3  &r,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &s,
 	     const typename K::Ray_3 &r,
 	     const K& k)
 {
   CGAL_precondition(! s.is_degenerate () && ! r.is_degenerate () );
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else 
   typename Intersection_traits<K, typename K::Line_3, typename K::Segment_3>::result_type 
-  #endif
     v = internal::intersection(r.supporting_line(),s, K());
 
   if(v) {
@@ -708,11 +627,7 @@ intersection(const typename K::Segment_3 &s,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &r,
 	     const typename K::Segment_3 &s,
 	     const K& k)
@@ -755,22 +670,14 @@ do_intersect(const typename K::Ray_3  &r,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &r1,
 	     const typename K::Ray_3 &r2,
 	     const K& k)
 {
   CGAL_precondition(! r1.is_degenerate () && ! r2.is_degenerate () );
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Line_3, typename K::Ray_3>::result_type 
-  #endif
     v = internal::intersection(r1.supporting_line(),r2, k);
 
   if(v) {
@@ -829,11 +736,7 @@ do_intersect(const typename K::Ray_3  &r1,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Sphere_3>::result_type
-#endif
 intersection(const typename K::Plane_3 &p,
              const typename K::Sphere_3 &s,
              const K&)
@@ -889,11 +792,7 @@ do_intersect(const typename K::Sphere_3 &s,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Sphere_3, typename K::Plane_3>::result_type
-#endif
 intersection(const typename K::Sphere_3 &s,
              const typename K::Plane_3 &p,
              const K& k)
@@ -903,11 +802,7 @@ intersection(const typename K::Sphere_3 &s,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Sphere_3, typename K::Sphere_3>::result_type
-#endif
 intersection(const typename K::Sphere_3 &s1,
              const typename K::Sphere_3 &s2,
              const K& k)
@@ -923,11 +818,7 @@ intersection(const typename K::Sphere_3 &s1,
   Plane_3 p = K().construct_radical_plane_3_object()(s1,s2);
   
   
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Sphere_3, typename K::Plane_3>::result_type 
-  #endif
     v = intersection(p, s1, k);
 
 
@@ -958,22 +849,14 @@ do_intersect(const typename K::Sphere_3 &s1,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Plane_3 &plane, 
 	     const typename K::Ray_3 &ray, 
 	     const K& k)
 {
     typedef typename K::Point_3 Point_3;
 
-    #if CGAL_INTERSECTION_VERSION < 2
-    CGAL::Object
-    #else
     typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type 
-    #endif
       v = internal::intersection(plane, ray.supporting_line(), k);
 
     if(v) {
@@ -993,11 +876,7 @@ intersection(const typename K::Plane_3 &plane,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Plane_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &ray, 
 	     const typename K::Plane_3 &plane, 
 	     const K& k)
@@ -1015,12 +894,8 @@ do_intersect(const typename K::Plane_3 &plane,
 {
     typedef typename K::Point_3 Point_3;
     
-    #if CGAL_INTERSECTION_VERSION < 2
-    CGAL::Object
-    #else
     typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>
       ::result_type 
-    #endif
       line_intersection = internal::intersection(plane, ray.supporting_line(), k);
 
     if(!line_intersection)
@@ -1044,11 +919,7 @@ do_intersect(const typename K::Ray_3 &ray,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Plane_3 &plane, 
 	     const typename K::Segment_3 &seg, 
 	     const K& k)
@@ -1076,11 +947,7 @@ intersection(const typename K::Plane_3 &plane,
           { 
             // intersection object should be a point, but rounding errors 
             // could lead to a line. In such case, return seg.
-            #if CGAL_INTERSECTION_VERSION < 2
-            CGAL::Object
-            #else
             typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type
-            #endif
               v = internal::intersection(plane, seg.supporting_line(), k);
             if(v) {
               if(const typename K::Point_3* p = intersect_get<typename K::Point_3>(v))
@@ -1098,11 +965,7 @@ intersection(const typename K::Plane_3 &plane,
           { 
             // intersection object should be a point, but rounding errors 
             // could lead to a line. In such case, return seg.
-            #if CGAL_INTERSECTION_VERSION < 2
-            CGAL::Object
-            #else
             typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type
-            #endif
               v = internal::intersection(plane, seg.supporting_line(), k);
             if(v) {
               if(const typename K::Point_3* p = intersect_get<typename K::Point_3>(v))
@@ -1122,11 +985,7 @@ intersection(const typename K::Plane_3 &plane,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Plane_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &seg, 
 	     const typename K::Plane_3 &plane, 
 	     const K& k)
@@ -1168,21 +1027,13 @@ do_intersect(const typename K::Segment_3 &seg,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Plane_3, typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Plane_3 &plane, 
 	     const typename K::Triangle_3 &tri, 
 	     const K& k)
 {
   typedef 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Plane_3, typename K::Line_3>::result_type 
-  #endif
   pl_res;
 
   typename K::Construct_vertex_3 vertex_on =
@@ -1277,11 +1128,7 @@ intersection(const typename K::Plane_3 &plane,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Plane_3>::result_type
-#endif
 intersection(const typename K::Triangle_3 &triangle,
 	     const typename K::Plane_3  &plane,
 	     const K& k)
@@ -1290,11 +1137,7 @@ intersection(const typename K::Triangle_3 &triangle,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, Bbox_3>::result_type
-#endif
 intersection(const typename K::Line_3 &line,
 	     const Bbox_3 &box, 
 	     const K&)
@@ -1317,11 +1160,7 @@ intersection(const typename K::Line_3 &line,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, Bbox_3, typename K::Line_3>::result_type
-#endif
 intersection(const Bbox_3 &box, 
 	     const typename K::Line_3 &line, 
 	     const K& k)
@@ -1331,11 +1170,7 @@ intersection(const Bbox_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, Bbox_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &ray,
 	     const Bbox_3 &box, 
 	     const K&)
@@ -1358,11 +1193,7 @@ intersection(const typename K::Ray_3 &ray,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, Bbox_3, typename K::Ray_3>::result_type
-#endif
 intersection(const Bbox_3 &box, 
 	     const typename K::Ray_3 &ray, 
 	     const K& k)
@@ -1373,11 +1204,7 @@ intersection(const Bbox_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, Bbox_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &seg, 
 	     const Bbox_3 &box, 
 	     const K&)
@@ -1400,11 +1227,7 @@ intersection(const typename K::Segment_3 &seg,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, Bbox_3, typename K::Segment_3>::result_type
-#endif
 intersection(const Bbox_3 &box, 
 	     const typename K::Segment_3 &seg, 
 	     const K& k)
@@ -1414,11 +1237,7 @@ intersection(const Bbox_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Line_3, typename K::Iso_cuboid_3>::result_type
-#endif
 intersection(const typename K::Line_3 &line,
 	     const typename K::Iso_cuboid_3 &box, 
 	     const K&)
@@ -1481,11 +1300,7 @@ intersection(const typename K::Line_3 &line,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Line_3>::result_type
-#endif
 intersection(const typename K::Iso_cuboid_3 &box, 
 	     const typename K::Line_3 &line, 
 	     const K& k)
@@ -1496,11 +1311,7 @@ intersection(const typename K::Iso_cuboid_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Iso_cuboid_3>::result_type
-#endif
 intersection(const typename K::Ray_3 &ray,
 	     const typename K::Iso_cuboid_3 &box, 
 	     const K&)
@@ -1562,11 +1373,7 @@ intersection(const typename K::Ray_3 &ray,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Iso_cuboid_3 &box, 
 	     const typename K::Ray_3 &ray,
 	     const K& k)
@@ -1576,11 +1383,7 @@ intersection(const typename K::Iso_cuboid_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Iso_cuboid_3>::result_type
-#endif
 intersection(const typename K::Segment_3 &seg,
 	     const typename K::Iso_cuboid_3 &box, 
 	     const K&)
@@ -1642,11 +1445,7 @@ intersection(const typename K::Segment_3 &seg,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Segment_3>::result_type
-#endif
 intersection(const typename K::Iso_cuboid_3 &box, 
 	     const typename K::Segment_3 &seg,
 	     const K& k)
@@ -1656,11 +1455,7 @@ intersection(const typename K::Iso_cuboid_3 &box,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Iso_cuboid_3, typename K::Iso_cuboid_3>::result_type
-#endif
 intersection(
     const typename K::Iso_cuboid_3 &icub1,
     const typename K::Iso_cuboid_3 &icub2, 
diff --git a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
index f0dfba3bed6..3d96fc2eaa4 100644
--- a/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
+++ b/Intersections_3/include/CGAL/Triangle_3_Triangle_3_intersection.h
@@ -61,13 +61,9 @@ void intersection_coplanar_triangles_cutoff(
     Orientation or_prev=orientations[prev],or_curr=orientations[&curr];
     if ( (or_prev==POSITIVE && or_curr==NEGATIVE) || (or_prev==NEGATIVE && or_curr==POSITIVE) )
     {
-      #if CGAL_INTERSECTION_VERSION < 2
-      CGAL::Object
-      #else
       typename Intersection_traits<Kernel, typename Kernel::Line_3,
                                      typename Kernel::Line_3>
         ::result_type 
-      #endif
         obj = intersection(Line_3(p,q),Line_3(*prev,curr),k);
       // assert "not empty"
       CGAL_kernel_assertion(obj);
@@ -92,11 +88,7 @@ void intersection_coplanar_triangles_cutoff(
 }
   
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>::result_type
-#endif
 intersection_coplanar_triangles(
   const typename K::Triangle_3& t1,
   const typename K::Triangle_3& t2,
@@ -133,12 +125,8 @@ intersection_coplanar_triangles(
 
 template<typename K>
 struct Triangle_Line_visitor {
-  #if CGAL_INTERSECTION_VERSION < 2
-  typedef CGAL::Object result_type;
-  #else
   typedef typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3 >
   ::result_type result_type;
-  #endif
 
   result_type
   operator()(const typename K::Point_3& p, const typename K::Segment_3&) const {
@@ -157,11 +145,7 @@ struct Triangle_Line_visitor {
 
   result_type
   operator()(const typename K::Segment_3& s1, const typename K::Segment_3& s2) const {
-    #if CGAL_INTERSECTION_VERSION < 2
-    CGAL::Object
-    #else
     typename Intersection_traits<K, typename K::Segment_3, typename K::Segment_3>::result_type 
-    #endif
       v = intersection_collinear_segments(s1,s2,K());
 
     if(v) {
@@ -176,11 +160,7 @@ struct Triangle_Line_visitor {
 };
   
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>::result_type
-#endif
 intersection(
   const typename K::Triangle_3& t1,
   const typename K::Triangle_3& t2,
@@ -188,11 +168,7 @@ intersection(
 {
   CGAL_precondition(!t1.is_degenerate() && !t2.is_degenerate());
 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Plane_3, typename K::Plane_3>::result_type 
-  #endif
     v = internal::intersection(t1.supporting_plane(), t2.supporting_plane(), k);
 
   if(!v) {
@@ -208,11 +184,7 @@ intersection(
   if(const typename K::Line_3* line=intersect_get<typename K::Line_3>(v)) {
     //The supporting planes of the triangles intersect along a line.
     typedef
-    #if CGAL_INTERSECTION_VERSION < 2
-    CGAL::Object
-    #else
     typename Intersection_traits<K, typename K::Triangle_3, typename K::Line_3>::result_type
-    #endif
       Triangle_Line_Inter;
     
     Triangle_Line_Inter inter1 = intersection_coplanar(t1,*line,k);
@@ -226,15 +198,15 @@ intersection(
     Triangle_Line_visitor<K> vis;
     if(const typename K::Point_3* p1 = intersect_get<typename K::Point_3>(inter1)) {
       if(const typename K::Point_3* p2 = intersect_get<typename K::Point_3>(inter2)) {
-        vis(*p1, *p2);
+        return vis(*p1, *p2);
       } else if(const typename K::Segment_3* s2 = intersect_get<typename K::Segment_3>(inter2)) {
-        vis(*p1, *s2);
+        return vis(*p1, *s2);
       }
     } else if(const typename K::Segment_3* s1 = intersect_get<typename K::Segment_3>(inter1)) {
       if(const typename K::Point_3* p2 = intersect_get<typename K::Point_3>(inter2)) {
-        vis(*s1, *p2);
+        return vis(*s1, *p2);
       } else if(const typename K::Segment_3* s2 = intersect_get<typename K::Segment_3>(inter2)) {
-        vis(*s1, *s2);
+        return vis(*s1, *s2);
       }
     }
     #else
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
index bda9ea03902..e42a18d8159 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Line_3_intersection.h
@@ -109,11 +109,7 @@ t3l3_intersection_coplanar_aux(const typename K::Point_3& a,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Line_3>::result_type
-#endif
 intersection_coplanar(const typename K::Triangle_3 &t,
                       const typename K::Line_3  &l,
                       const K & k )
@@ -314,11 +310,7 @@ intersection_coplanar(const typename K::Triangle_3 &t,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits<K, typename K::Line_3, typename K::Triangle_3>::result_type
-#endif
 t3l3_intersection_aux(const typename K::Triangle_3 &t,
                       const typename K::Line_3 &l,
                       const K&)
@@ -327,11 +319,7 @@ t3l3_intersection_aux(const typename K::Triangle_3 &t,
   //   k.intersect_3_object();
 
   // The intersection between a Line and Plane is either Point or Line
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Line_3, typename K::Plane_3>::result_type 
-  #endif
     v = internal::intersection(l,t.supporting_plane(), K());
   
   // Intersection should be a point (because of orientation test done before)
@@ -348,11 +336,7 @@ t3l3_intersection_aux(const typename K::Triangle_3 &t,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits<K, typename K::Line_3, typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Triangle_3 &t,
              const typename K::Line_3 &l,
              const K& k)
@@ -428,11 +412,7 @@ intersection(const typename K::Triangle_3 &t,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename CGAL::Intersection_traits<K, typename K::Line_3, typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Line_3 &l,
              const typename K::Triangle_3 &t,
              const K& k)
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
index 903066b0586..81979f0f833 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Ray_3_intersection.h
@@ -70,14 +70,8 @@ t3r3_intersection_coplanar_aux(const typename K::Point_3& p,
 }
 
 
-// the return type is the same as the intersection(Triangle Ray). We
-// spell it out here for clarity.
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
-typename boost::optional< boost::variant< typename K::Point_3, typename K::Segment_3> >
-#endif
+typename IT<K, typename K::Triangle_3, typename K::Ray_3>::result_type
 t3r3_intersection_coplanar_aux(const typename K::Point_3& a,
                                const typename K::Point_3& b,
                                const typename K::Point_3& c,
@@ -167,14 +161,8 @@ t3r3_intersection_coplanar_aux(const typename K::Point_3& a,
   return intersection_return<K, typename K::Triangle_3, typename K::Ray_3>();
 }
 
-// the return type is the same as the intersection(Triangle Ray). We
-// spell it out here for clarity.
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
-typename boost::optional< boost::variant< typename K::Point_3, typename K::Segment_3> >
-#endif
+typename IT<K, typename K::Triangle_3, typename K::Ray_3>::result_type
 intersection_coplanar(const typename K::Triangle_3 &t,
                       const typename K::Ray_3  &r,
                       const K & k )
@@ -441,12 +429,8 @@ t3r3_intersection_aux(const typename K::Triangle_3 &t,
                       const typename K::Ray_3 &r,
                       const K& k)
 {
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename Intersection_traits<K, typename K::Line_3, typename K::Plane_3>
     ::result_type 
-  #endif
     v = internal::intersection(r.supporting_line(),t.supporting_plane(), k);
 
   if(v) {
@@ -458,12 +442,8 @@ t3r3_intersection_aux(const typename K::Triangle_3 &t,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3,
                                typename K::Ray_3>::result_type
-#endif
 intersection(const typename K::Triangle_3  &t,
              const typename K::Ray_3 &r,
              const K& k)
@@ -604,11 +584,7 @@ intersection(const typename K::Triangle_3  &t,
 }
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Ray_3, typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Ray_3  &r,
              const typename K::Triangle_3 &t,
              const K& k) {
diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
index fd2264faeee..e0e480f4341 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Triangle_3_Segment_3_intersection.h
@@ -72,11 +72,7 @@ t3s3_intersection_coplanar_aux(const typename K::Point_3& p,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Segment_3>::result_type
-#endif
 t3s3_intersection_coplanar_aux(const typename K::Point_3& a,
                                const typename K::Point_3& b,
                                const typename K::Point_3& c,
@@ -142,11 +138,7 @@ t3s3_intersection_coplanar_aux(const typename K::Point_3& a,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Triangle_3, typename K::Segment_3>::result_type
-#endif
 t3s3_intersection_collinear_aux(const typename K::Point_3& a,
                                 const typename K::Point_3& b,
                                 const typename K::Point_3& p,
@@ -188,11 +180,7 @@ t3s3_intersection_collinear_aux(const typename K::Point_3& a,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Triangle_3>::result_type
-#endif
 intersection_coplanar(const typename K::Triangle_3 &t,
                       const typename K::Segment_3  &s,
                       const K & k )
@@ -406,11 +394,7 @@ intersection_coplanar(const typename K::Triangle_3 &t,
 
 
 template <class K>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Triangle_3 &t,
              const typename K::Segment_3  &s,
              const K & k)
@@ -457,12 +441,8 @@ intersection(const typename K::Triangle_3 &t,
           {
             // The intersection should be a point
             
-            #if CGAL_INTERSECTION_VERSION < 2
-            CGAL::Object
-            #else 
             typename Intersection_traits<K, typename K::Line_3, typename K::Plane_3>
               ::result_type 
-            #endif
               v = internal::intersection(s.supporting_line(),t.supporting_plane(), K());
             if(v) {
               if(const Point_3* res = intersect_get<Point_3>(v))
@@ -498,11 +478,7 @@ intersection(const typename K::Triangle_3 &t,
             && orientation(q,p,b,c) != POSITIVE
             && orientation(q,p,c,a) != POSITIVE )
           {
-            #if CGAL_INTERSECTION_VERSION < 2
-            CGAL::Object
-            #else
             typename Intersection_traits<K, typename K::Line_3, typename K::Plane_3>::result_type 
-            #endif
               v = internal::intersection(s.supporting_line(),t.supporting_plane(), K());
             if(v) {
               if(const Point_3* res = intersect_get<Point_3>(v))
@@ -571,12 +547,8 @@ intersection(const typename K::Triangle_3 &t,
 
 template <class K>
 inline
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename Intersection_traits<K, typename K::Segment_3, 
                                typename K::Triangle_3>::result_type
-#endif
 intersection(const typename K::Segment_3  &s,
              const typename K::Triangle_3 &t,
              const K & k)
diff --git a/Intersections_3/include/CGAL/intersection_3_0.h b/Intersections_3/include/CGAL/intersection_3_0.h
index 2f9cde4b92c..1f361a98be0 100644
--- a/Intersections_3/include/CGAL/intersection_3_0.h
+++ b/Intersections_3/include/CGAL/intersection_3_0.h
@@ -44,11 +44,7 @@ namespace CGAL {
   // intersections with Bbox_3 for which no kernel traits exist
   template<class A>
   inline 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename IT< typename CGAL::Kernel_traits<A>::Kernel, A, CGAL::Bbox_3 >::result_type
-  #endif
   intersection(const A& a, const CGAL::Bbox_3& b) {
     typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
     return Kernel().intersect_3_object()(a, b);
@@ -56,11 +52,7 @@ namespace CGAL {
 
   template<class A>
   inline 
-  #if CGAL_INTERSECTION_VERSION < 2
-  CGAL::Object
-  #else
   typename IT< typename CGAL::Kernel_traits<A>::Kernel, A, CGAL::Bbox_3 >::result_type
-  #endif
   intersection(const CGAL::Bbox_3& b, const A& a) {
     typedef typename CGAL::Kernel_traits<A>::Kernel Kernel;
     return Kernel().intersect_3_object()(a, b);
diff --git a/Kernel_d/include/CGAL/Intersection_traits_d.h b/Kernel_d/include/CGAL/Intersection_traits_d.h
index 0c4e9cc9e35..b5806b67775 100644
--- a/Kernel_d/include/CGAL/Intersection_traits_d.h
+++ b/Kernel_d/include/CGAL/Intersection_traits_d.h
@@ -23,31 +23,35 @@
 
 #include <CGAL/Intersection_traits.h>
 
+#if !(CGAL_INTERSECTION_VERSION < 2)
+
 namespace CGAL {
   
-  CGAL_INTERSECTION_TRAITS_2(Line_d, Line_d, Point_d, Line_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Line_d, Line_d, Point_d, Line_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Segment_d, Line_d, Point_d, Segment_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Line_d, Segment_d, Point_d, Segment_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Segment_d, Line_d, Point_d, Segment_d)
+  CGAL_INTERSECTION_TRAITS_2(Line_d, Segment_d, Point_d, Segment_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Segment_d, Segment_d, Point_d, Segment_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Segment_d, Segment_d, Point_d, Segment_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Ray_d, Line_d, Point_d, Ray_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Line_d, Ray_d, Point_d, Ray_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Ray_d, Line_d, Point_d, Ray_d)
+  CGAL_INTERSECTION_TRAITS_2(Line_d, Ray_d, Point_d, Ray_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Ray_d, Segment_d, Point_d, Segment_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Segment_d, Ray_d, Point_d, Segment_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Ray_d, Segment_d, Point_d, Segment_d)
+  CGAL_INTERSECTION_TRAITS_2(Segment_d, Ray_d, Point_d, Segment_d)
 
-  CGAL_INTERSECTION_TRAITS_3(Ray_d, Ray_d, Point_d, Segment_d, Ray_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_3(Ray_d, Ray_d, Point_d, Segment_d, Ray_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Line_d, Point_d, Line_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Line_d, Hyperplane_d, Point_d, Line_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Line_d, Point_d, Line_d)
+  CGAL_INTERSECTION_TRAITS_2(Line_d, Hyperplane_d, Point_d, Line_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Ray_d, Point_d, Ray_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Ray_d, Hyperplane_d, Point_d, Ray_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Ray_d, Point_d, Ray_d)
+  CGAL_INTERSECTION_TRAITS_2(Ray_d, Hyperplane_d, Point_d, Ray_d)
 
-  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Segment_d, Point_d, Segment_d, Intersection_dim_d)
-  CGAL_INTERSECTION_TRAITS_2(Segment_d, Hyperplane_d, Point_d, Segment_d, Intersection_dim_d)
+  CGAL_INTERSECTION_TRAITS_2(Hyperplane_d, Segment_d, Point_d, Segment_d)
+  CGAL_INTERSECTION_TRAITS_2(Segment_d, Hyperplane_d, Point_d, Segment_d)
 }
 
+#endif // !(CGAL_INTERSECTION_VERSION < 2)
+
 #endif /* CGAL_INTERSECTION_TRAITS_D_H */
diff --git a/Kernel_d/include/CGAL/intersections_d.h b/Kernel_d/include/CGAL/intersections_d.h
index 2ee3ef23d8e..81e6e80261e 100644
--- a/Kernel_d/include/CGAL/intersections_d.h
+++ b/Kernel_d/include/CGAL/intersections_d.h
@@ -34,11 +34,7 @@ namespace CGAL {
 namespace internal {
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Line_d, typename R::Line_d>::result_type
-#endif
 intersection(const typename R::Line_d& l1, const typename R::Line_d& l2, const R&)
 { 
   typedef typename R::Line_d_Line_d_pair ll_pair;
@@ -59,11 +55,7 @@ intersection(const typename R::Line_d& l1, const typename R::Line_d& l2, const R
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Ray_d, typename R::Ray_d>::result_type 
-#endif
 intersection(const typename R::Ray_d& l1, const typename R::Ray_d& l2, const R&)
 { 
   typedef typename R::Ray_d_Ray_d_pair ll_pair;
@@ -92,11 +84,7 @@ intersection(const typename R::Ray_d& l1, const typename R::Ray_d& l2, const R&)
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Segment_d, typename R::Segment_d>::result_type
-#endif
 intersection(const typename R::Segment_d& l1, const typename R::Segment_d& l2, const R&)
 {
   typedef typename R::Segment_d_Segment_d_pair ll_pair;
@@ -120,11 +108,7 @@ intersection(const typename R::Segment_d& l1, const typename R::Segment_d& l2, c
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Line_d, typename R::Ray_d>::result_type
-#endif
 intersection(const typename R::Line_d& l, const typename R::Ray_d& r, const R&)
 {
   typedef typename R::Line_d_Ray_d_pair lr_pair;
@@ -146,20 +130,12 @@ intersection(const typename R::Line_d& l, const typename R::Ray_d& r, const R&)
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Ray_d, typename R::Line_d>::result_type
-#endif
 intersection(const typename R::Ray_d& r, const typename R::Line_d& l, const R& k)
 { return intersection(l,r,k); }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Ray_d, typename R::Segment_d>::result_type
-#endif
 intersection(const typename R::Ray_d& r, const typename R::Segment_d& s, const R&)
 {
   typedef typename R::Ray_d_Segment_d_pair rs_pair;
@@ -183,20 +159,12 @@ intersection(const typename R::Ray_d& r, const typename R::Segment_d& s, const R
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Segment_d, typename R::Ray_d>::result_type
-#endif
 intersection(const typename R::Segment_d& s, const typename R::Ray_d& r, const R& k)
 { return intersection(r,s, k); }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Line_d, typename R::Segment_d>::result_type
-#endif
 intersection(const typename R::Line_d& l, const typename R::Segment_d& s, const R&)
 {
   typedef typename R::Line_d_Segment_d_pair rs_pair;
@@ -220,20 +188,12 @@ intersection(const typename R::Line_d& l, const typename R::Segment_d& s, const
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Segment_d, typename R::Line_d>::result_type
-#endif
 intersection(const typename R::Segment_d& s, const typename R::Line_d& l, const R& r)
 { return intersection(l,s,r); }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Line_d, typename R::Hyperplane_d>::result_type
-#endif
 intersection(const typename R::Line_d& l, const typename R::Hyperplane_d& h, const R&)
 {
   typedef typename R::Line_d_Hyperplane_d_pair lh_pair;
@@ -254,20 +214,12 @@ intersection(const typename R::Line_d& l, const typename R::Hyperplane_d& h, con
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Hyperplane_d, typename R::Line_d>::result_type
-#endif
 intersection(const typename R::Hyperplane_d& h, const typename R::Line_d& l, const R& r)
 { return intersection(l,h,r); }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Ray_d, typename R::Hyperplane_d>::result_type
-#endif
 intersection(const typename R::Ray_d& r, const typename R::Hyperplane_d& h, const R&)
 {
   typedef typename R::Ray_d_Hyperplane_d_pair rh_pair;
@@ -288,20 +240,12 @@ intersection(const typename R::Ray_d& r, const typename R::Hyperplane_d& h, cons
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Hyperplane_d, typename R::Ray_d>::result_type
-#endif
 intersection(const typename R::Hyperplane_d& h, const typename R::Ray_d& r, const R& k)
 { return intersection(r,h,k); }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Segment_d, typename R::Hyperplane_d>::result_type
-#endif
 intersection(const typename R::Segment_d& s, const typename R::Hyperplane_d& h, const R&)
 {
   typedef typename R::Segment_d_Hyperplane_d_pair sh_pair;
@@ -322,11 +266,7 @@ intersection(const typename R::Segment_d& s, const typename R::Hyperplane_d& h,
 }
 
 template <class R>
-#if CGAL_INTERSECTION_VERSION < 2
-CGAL::Object
-#else
 typename IT<R, typename R::Hyperplane_d, typename R::Segment_d>::result_type
-#endif
 intersection(const typename R::Hyperplane_d& h, const typename R::Segment_d& s, const R& r)
 { return intersection(s,h,r); }