diff --git a/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_intersection_example.cpp b/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_intersection_example.cpp
index 9d483301d30..4b615ca52f4 100644
--- a/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_intersection_example.cpp
+++ b/AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_intersection_example.cpp
@@ -17,8 +17,8 @@ typedef CGAL::Polyhedron_3<K> Polyhedron;
 typedef CGAL::AABB_polyhedron_triangle_primitive<K,Polyhedron> Primitive;
 typedef CGAL::AABB_traits<K, Primitive> Traits;
 typedef CGAL::AABB_tree<Traits> Tree;
-typedef Tree::Intersection_and_primitive_id<Segment>::Type Segment_intersection;
-typedef Tree::Intersection_and_primitive_id<Plane>::Type Plane_intersection;
+typedef boost::optional< Tree::Intersection_and_primitive_id<Segment>::Type > Segment_intersection;
+typedef boost::optional< Tree::Intersection_and_primitive_id<Plane>::Type > Plane_intersection;
 typedef Tree::Primitive_id Primitive_id;
 
 int main()
@@ -52,10 +52,10 @@ int main()
     // (generally a point)
     Segment_intersection intersection =
         tree.any_intersection(segment_query);
-    if(intersection.first)
+    if(intersection)
     {
         // gets intersection object
-      if(boost::get<Point>(&*intersection.first))
+      if(boost::get<Point>(&(intersection->first)))
         std::cout << "intersection object is a point" << std::endl;
     }
 
@@ -74,10 +74,10 @@ int main()
     // computes first encountered intersection with plane query
     // (generally a segment)
     Plane_intersection plane_intersection = tree.any_intersection(plane_query);
-    if(plane_intersection.first)
+    if(plane_intersection)
     {
       
-      if(boost::get<Segment>(&*plane_intersection.first))
+      if(boost::get<Segment>(&(plane_intersection->first)))
             std::cout << "intersection object is a segment" << std::endl;
     }
 
diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index 3f873a16660..d6e1f2ac335 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -71,9 +71,8 @@ public:
   template<typename Query>
   struct Intersection_and_primitive_id {
     typedef std::pair< 
-      typename cpp11::result_of<typename GeomTraits::Intersect_3(Query, typename Primitive::Datum) >::type, 
+      typename IT<Query, typename Primitive::Datum>::variant_type, //using Intersection_traits to skip the optional
       typename Primitive::Id > Type;
-    typedef Type type;
   };
 
   // types for search tree
@@ -206,10 +205,13 @@ operator()(const Query& query, const typename AT::Primitive& primitive) const
 }
     #else
     template<typename Query>
-    typename Intersection_and_primitive_id<Query>::Type
+    boost::optional< typename Intersection_and_primitive_id<Query>::Type >
     operator()(const Query& query, const typename AT::Primitive& primitive) const {
-      return std::make_pair(GeomTraits().intersect_3_object()(primitive.datum(),query), 
-                            primitive.id());
+      typename cpp11::result_of<typename GeomTraits::Intersect_3(Query, typename Primitive::Datum) >::type
+        inter_res = GeomTraits().intersect_3_object()(primitive.datum(),query);
+      if (!inter_res)
+          return boost::optional<typename Intersection_and_primitive_id<Query>::Type>();
+      return boost::make_optional( std::make_pair(*inter_res, primitive.id()) );
     }
     #endif
 };
diff --git a/AABB_tree/include/CGAL/AABB_tree.h b/AABB_tree/include/CGAL/AABB_tree.h
index 62922953332..ce637c52880 100644
--- a/AABB_tree/include/CGAL/AABB_tree.h
+++ b/AABB_tree/include/CGAL/AABB_tree.h
@@ -262,7 +262,7 @@ public:
     #if CGAL_INTERSECTION_VERSION < 2
 		boost::optional<Object_and_primitive_id> 
     #else
-    typename Intersection_and_primitive_id<Query>::Type
+    boost::optional< typename Intersection_and_primitive_id<Query>::Type >
     #endif
     any_intersection(const Query& query) const;
 
@@ -706,7 +706,7 @@ public:
   #if CGAL_INTERSECTION_VERSION < 2
 	boost::optional<typename AABB_tree<Tr>::Object_and_primitive_id>
   #else
-  typename AABB_tree<Tr>::template Intersection_and_primitive_id<Query>::Type
+  boost::optional< typename AABB_tree<Tr>::template Intersection_and_primitive_id<Query>::Type >
   #endif
 		AABB_tree<Tr>::any_intersection(const Query& query) const
 	{
diff --git a/AABB_tree/include/CGAL/internal/AABB_tree/AABB_traversal_traits.h b/AABB_tree/include/CGAL/internal/AABB_tree/AABB_traversal_traits.h
index 3c1fc18e58c..4cfb2926c0e 100644
--- a/AABB_tree/include/CGAL/internal/AABB_tree/AABB_traversal_traits.h
+++ b/AABB_tree/include/CGAL/internal/AABB_tree/AABB_traversal_traits.h
@@ -73,11 +73,11 @@ class First_intersection_traits
   typedef ::CGAL::AABB_node<AABBTraits> Node;
 
 public:
-  typedef typename 
+  typedef
   #if CGAL_INTERSECTION_VERSION < 2
   boost::optional<Object_and_primitive_id> 
   #else
-  AABBTraits::template Intersection_and_primitive_id<Query>::Type
+  boost::optional< typename AABBTraits::template Intersection_and_primitive_id<Query>::Type >
   #endif
   Result;
 public:
@@ -86,11 +86,7 @@ public:
   {}
 
   bool go_further() const { 
-    #if CGAL_INTERSECTION_VERSION < 2
     return !m_result;
-    #else
-    return !m_result.first; 
-    #endif
   }
 
   void intersection(const Query& query, const Primitive& primitive)
@@ -105,11 +101,7 @@ public:
 
   Result result() const { return m_result; }
   bool is_intersection_found() const { 
-    #if CGAL_INTERSECTION_VERSION < 2
     return m_result;
-    #else
-    return m_result.first;
-    #endif
   }
 
 private:
@@ -143,21 +135,14 @@ public:
     #if CGAL_INTERSECTION_VERSION < 2
     boost::optional<Object_and_primitive_id>
     #else
-    typename AABBTraits::template Intersection_and_primitive_id<Query>::Type 
+    boost::optional< typename AABBTraits::template Intersection_and_primitive_id<Query>::Type >
     #endif
     intersection = AABBTraits().intersection_object()(query, primitive);
 
-    #if CGAL_INTERSECTION_VERSION < 2
     if(intersection)
     {
       *m_out_it++ = *intersection;
     }
-    #else
-    if(intersection.first)
-    {
-      *m_out_it++ = intersection;
-    }
-    #endif
   }
 
   bool do_intersect(const Query& query, const Node& node) const
diff --git a/AABB_tree/test/AABB_tree/AABB_test_util.h b/AABB_tree/test/AABB_tree/AABB_test_util.h
index 1df1f612569..c790aa7d802 100644
--- a/AABB_tree/test/AABB_tree/AABB_test_util.h
+++ b/AABB_tree/test/AABB_tree/AABB_test_util.h
@@ -106,9 +106,9 @@ void test_all_intersection_query_types(Tree& tree)
     optional_object_and_primitive = tree.any_intersection(line);
     optional_object_and_primitive = tree.any_intersection(segment);
     #else
-    typename Tree::AABB_traits::template Intersection_and_primitive_id<Ray>::type r = tree.any_intersection(ray);
-    typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::type l = tree.any_intersection(line);    
-    typename Tree::AABB_traits::template Intersection_and_primitive_id<Segment>::type s = tree.any_intersection(segment);
+    boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Ray>::Type > r = tree.any_intersection(ray);
+    boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::Type > l = tree.any_intersection(line);    
+    boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Segment>::Type > s = tree.any_intersection(segment);
     #endif
 
     // any_intersected_primitive
@@ -124,9 +124,9 @@ void test_all_intersection_query_types(Tree& tree)
     tree.all_intersections(line,std::back_inserter(intersections));
     tree.all_intersections(segment,std::back_inserter(intersections));
     #else
-    std::list<typename Tree::AABB_traits::template Intersection_and_primitive_id<Ray>::type> intersections_r;
-    std::list<typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::type> intersections_l;
-    std::list<typename Tree::AABB_traits::template Intersection_and_primitive_id<Segment>::type> intersections_s;
+    std::list< boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Ray>::Type > > intersections_r;
+    std::list< boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::Type > > intersections_l;
+    std::list< boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Segment>::Type > > intersections_s;
     tree.all_intersections(ray,std::back_inserter(intersections_r));
     tree.all_intersections(line,std::back_inserter(intersections_l));
     tree.all_intersections(segment,std::back_inserter(intersections_s));
@@ -389,14 +389,12 @@ public:
       #if CGAL_INTERSECTION_VERSION < 2
       Intersection_result 
         intersection  = Traits().intersection_object()(query, Pr(it));
+      #else
+      boost::optional< typename Traits::template Intersection_and_primitive_id<Query>::Type >
+        intersection  = Traits().intersection_object()(query, Pr(it));
+      #endif
       if ( intersection )
         *out++ = *intersection;
-      #else
-      typename Traits::template Intersection_and_primitive_id<Query>::type
-        intersection  = Traits().intersection_object()(query, Pr(it));
-      if ( intersection.first )
-        *out++ = intersection;
-      #endif                           
     }
 
     return out;
@@ -704,7 +702,7 @@ private:
         #if CGAL_INTERSECTION_VERSION < 2
         Object_and_primitive_id
         #else
-        typename Tree::AABB_traits::template Intersection_and_primitive_id<Query>::type
+        typename Tree::AABB_traits::template Intersection_and_primitive_id<Query>::Type
         #endif
         Obj_type;
 
@@ -746,12 +744,11 @@ private:
       #if CGAL_INTERSECTION_VERSION < 2
       boost::optional<Object_and_primitive_id>
       #else
-      typename Tree::AABB_traits::template Intersection_and_primitive_id<Query>::type 
+      boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Query>::Type >
       #endif
         intersection = tree.any_intersection(query);
 
       // Check: verify we do get the result by naive method
-      #if CGAL_INTERSECTION_VERSION < 2
       if ( intersection )
       {
         assert( std::find(intersections_naive_id.begin(),
@@ -759,15 +756,6 @@ private:
                           intersection->second)
                != intersections_naive_id.end());
       }
-      #else
-      if ( intersection.first )
-      {
-        assert( std::find(intersections_naive_id.begin(),
-                          intersections_naive_id.end(),
-                          intersection.second)
-               != intersections_naive_id.end());
-      }
-      #endif
       else if ( intersections_naive.size() != 0 )
         assert(false);
 
diff --git a/AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp b/AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp
index 8183a054701..bf3e994aa83 100644
--- a/AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp
+++ b/AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp
@@ -42,7 +42,7 @@ std::size_t intersect(ForwardIterator b, ForwardIterator e, const Tree& tree, lo
 #if CGAL_INTERSECTION_VERSION < 2
         typename Tree::Object_and_primitive_id
 #else
-        typename Tree::AABB_traits::template Intersection_and_primitive_id<typename ForwardIterator::value_type>::type
+        typename Tree::AABB_traits::template Intersection_and_primitive_id<typename ForwardIterator::value_type>::Type
 #endif
         Obj_type;
 
@@ -51,16 +51,9 @@ std::size_t intersect(ForwardIterator b, ForwardIterator e, const Tree& tree, lo
   v.reserve(elements);
   for(; b != e; ++b) {
     tree.all_intersections(*b, std::back_inserter(v));
-#if CGAL_INTERSECTION_VERSION < 2
     boost::optional<Obj_type> o = tree.any_intersection(*b);
     if(o)
       ++counter;
-#else
-    Obj_type
-      o = tree.any_intersection(*b);
-    if(o.first)
-      ++counter;
-#endif
   }
 
   return v.size();
diff --git a/Filtered_kernel/test/Filtered_kernel/test_lazy_vector_objects.cpp b/Filtered_kernel/test/Filtered_kernel/test_lazy_vector_objects.cpp
index a634e1281cc..ad47d41b3e0 100644
--- a/Filtered_kernel/test/Filtered_kernel/test_lazy_vector_objects.cpp
+++ b/Filtered_kernel/test/Filtered_kernel/test_lazy_vector_objects.cpp
@@ -35,7 +35,7 @@ int main()
     obj = CGAL::intersection(s1,s2);
 
     // check the variant return type
-    K::Intersect_2::Result<Triangle_2, Triangle_2>::Type o_variant = CGAL::intersection(t1,t2);
+    CGAL::cpp11::result_of<K::Intersect_2(Triangle_2, Triangle_2) >::type o_variant = CGAL::intersection(t1,t2);
     if(!o_variant) {
       std::cerr << "ERROR, empty" << std::endl;
       return EXIT_FAILURE;
@@ -75,7 +75,7 @@ int main()
     }
 
     // check the variant return type
-    K::Intersect_3::Result<Triangle_3, Triangle_3>::Type o_variant = CGAL::intersection(t1,t2);
+    CGAL::cpp11::result_of<K::Intersect_3(Triangle_3, Triangle_3)>::type o_variant = CGAL::intersection(t1,t2);
     if(!o_variant) {
       std::cerr << "ERROR, empty" << std::endl;
       return EXIT_FAILURE;
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
index 21b497fd593..be7d62af5e1 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
@@ -402,7 +402,7 @@ public:
                               Intersection>::type
     operator()(const Query& q) const
     {
-      typedef typename AABB_tree_::template Intersection_and_primitive_id<Query>::Type AABB_intersection;
+      typedef boost::optional< typename AABB_tree_::template Intersection_and_primitive_id<Query>::Type > AABB_intersection;
 
       typedef Point_3 Bare_point;
 
@@ -413,18 +413,18 @@ public:
         AABB_intersection() :
         r_domain_.bounding_tree_->any_intersection(q);
 
-      if(! intersection.first && 
+      if(! intersection && 
          r_domain_.bounding_tree_ != &r_domain_.tree_) {
         intersection = r_domain_.tree_.any_intersection(q);
       }
-      if ( intersection.first )
+      if ( intersection )
       {
         // Get primitive
-        AABB_primitive_id primitive_id = intersection.second;
+        AABB_primitive_id primitive_id = intersection->second;
         
         // intersection may be either a point or a segment
         if ( const Bare_point* p_intersect_pt =
-             boost::get<Bare_point>(&*intersection.first) )
+             boost::get<Bare_point>( &(intersection->first) ) )
         {
           return Intersection(*p_intersect_pt,
                               r_domain_.index_from_surface_patch_index(
@@ -432,7 +432,7 @@ public:
                               2);
         }
         else if ( const Segment_3* p_intersect_seg =
-                  boost::get<Segment_3>(&*intersection.first))
+                  boost::get<Segment_3>(&(intersection->first)))
         {
           return Intersection(p_intersect_seg->source(),
                               r_domain_.index_from_surface_patch_index(
diff --git a/Polyhedron/demo/Polyhedron/include/CGAL/AABB_polyhedral_oracle.h b/Polyhedron/demo/Polyhedron/include/CGAL/AABB_polyhedral_oracle.h
index 2c4925a382e..4dfd5a0867d 100644
--- a/Polyhedron/demo/Polyhedron/include/CGAL/AABB_polyhedral_oracle.h
+++ b/Polyhedron/demo/Polyhedron/include/CGAL/AABB_polyhedral_oracle.h
@@ -94,44 +94,48 @@ namespace CGAL {
       Object operator()(const Surface_3& surface, const Segment_3& segment) const
       {
         #if CGAL_INTERSECTION_VERSION < 2
-        AABB_intersection intersection = surface.tree()->any_intersection(segment);
-      
-        if ( intersection )
-          return intersection->first;
-        else
-          return Object();
+        AABB_intersection
         #else
-        return (surface.tree()->any_intersection(segment)).first;
+        boost::optional< typename AABB_traits::template Intersection_and_primitive_id<Segment_3>::Type >
         #endif
-      }
-
-      Object operator()(const Surface_3& surface, const Ray_3& ray) const
-      {
-        #if CGAL_INTERSECTION_VERSION < 2
-        AABB_intersection intersection = surface.tree()->any_intersection(segment);
+          intersection = surface.tree()->any_intersection(segment);
         
         if ( intersection )
           return intersection->first;
         else
           return Object();
-        #else
-        return (surface.tree()->any_intersection(ray)).first;
-        #endif
       }
-
+      
       Object operator()(const Surface_3& surface, const Line_3& line) const
       {
         #if CGAL_INTERSECTION_VERSION < 2
-        AABB_intersection intersection = surface.tree()->any_intersection(segment);
+        AABB_intersection
+        #else
+        boost::optional< typename AABB_traits::template Intersection_and_primitive_id<Line_3>::Type >
+        #endif
+          intersection = surface.tree()->any_intersection(line);
         
         if ( intersection )
           return intersection->first;
         else
           return Object();
-        #else
-        return (surface.tree()->any_intersection(line)).first;
-        #endif
       }
+      Object operator()(const Surface_3& surface, const Ray_3& ray) const
+      {
+        #if CGAL_INTERSECTION_VERSION < 2
+        AABB_intersection
+        #else
+        boost::optional< typename AABB_traits::template Intersection_and_primitive_id<Ray_3>::Type >
+        #endif
+          intersection = surface.tree()->any_intersection(ray);
+        
+        if ( intersection )
+          return intersection->first;
+        else
+          return Object();
+      }
+
+
     };
 
     Intersect_3 intersect_3_object() const