diff --git a/Cartesian_kernel/include/CGAL/Cartesian.h b/Cartesian_kernel/include/CGAL/Cartesian.h
index 41af5cf7b48..3f5de1d9dd7 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian.h
@@ -51,6 +51,9 @@ struct Cartesian_base_ref_count
 #define CGAL_Kernel_cons(Y,Z) CGAL_Kernel_pred(Y,Z)
 
 #include <CGAL/Kernel/interface_macros.h>
+
+    template<typename A, typename B>
+    struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 template < typename FT_ >
diff --git a/Cartesian_kernel/include/CGAL/Simple_cartesian.h b/Cartesian_kernel/include/CGAL/Simple_cartesian.h
index 13a6160d241..c107e8b82a7 100644
--- a/Cartesian_kernel/include/CGAL/Simple_cartesian.h
+++ b/Cartesian_kernel/include/CGAL/Simple_cartesian.h
@@ -50,6 +50,9 @@ struct Cartesian_base_no_ref_count
 #define CGAL_Kernel_cons(Y,Z) CGAL_Kernel_pred(Y,Z)
 
 #include <CGAL/Kernel/interface_macros.h>
+
+    template<typename A, typename B>
+    struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 template < typename FT_ >
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
index 571828329d7..fb7e0cf9a02 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
@@ -80,9 +80,11 @@ struct Circular_kernel_base_ref_count: public LinearKernelBase
 
   #include <CGAL/Circular_kernel_2/interface_macros.h>
 
-	typedef LinearFunctors::Construct_line_2<CircularKernel> Construct_line_2;
+  typedef LinearFunctors::Construct_line_2<CircularKernel> Construct_line_2;
   Construct_line_2 construct_line_2_object() const { return Construct_line_2(); }
 
+  template<typename A, typename B>
+  struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 } // namespace internal
diff --git a/Circular_kernel_2/include/CGAL/Filtered_bbox_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Filtered_bbox_circular_kernel_2.h
index 9eb6f6d0ff3..0f0d5a37122 100644
--- a/Circular_kernel_2/include/CGAL/Filtered_bbox_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Filtered_bbox_circular_kernel_2.h
@@ -65,6 +65,8 @@ struct Filtered_bbox_circular_kernel_base_ref_count : public CircularKernel
 
   #include <CGAL/Filtered_bbox_circular_kernel_2/interface_macros.h>
 
+  template<typename A, typename B>
+  struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 } // namespace internal
diff --git a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
index 389a1dc5e61..160ffc9925f 100644
--- a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
@@ -74,6 +74,9 @@ struct Circular_kernel_base_ref_count: public LinearKernelBase
   #define CGAL_Circular_Kernel_cons(Y,Z) CGAL_Circular_Kernel_pred(Y,Z)
 
   #include <CGAL/Circular_kernel_2/interface_macros.h>
+
+  template<typename A, typename B>
+  struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 } // namespace internal
diff --git a/Circular_kernel_3/include/CGAL/Simple_spherical_kernel_3.h b/Circular_kernel_3/include/CGAL/Simple_spherical_kernel_3.h
index 17b505a8c30..4d963dbf42a 100644
--- a/Circular_kernel_3/include/CGAL/Simple_spherical_kernel_3.h
+++ b/Circular_kernel_3/include/CGAL/Simple_spherical_kernel_3.h
@@ -68,6 +68,9 @@ namespace CGAL {
         
         
         #include <CGAL/Circular_kernel_3/interface_macros.h>
+
+        template<typename A, typename B>
+        struct Intersection_result : CGAL::Intersection_traits<SphericalKernel, A, B> {};
       };
     
   } // namespace internal
diff --git a/Circular_kernel_3/include/CGAL/Spherical_kernel_3.h b/Circular_kernel_3/include/CGAL/Spherical_kernel_3.h
index 9e40c310bca..743acec9e96 100644
--- a/Circular_kernel_3/include/CGAL/Spherical_kernel_3.h
+++ b/Circular_kernel_3/include/CGAL/Spherical_kernel_3.h
@@ -66,6 +66,9 @@ namespace CGAL {
 	    Y Z(const CGAL::Sphere_3<SphericalKernel>& S) const { return Y(S); }
         
         #include <CGAL/Circular_kernel_3/interface_macros.h>
+
+        template<typename A, typename B>
+        struct Intersection_result : CGAL::Intersection_traits<SphericalKernel, A, B> {};
       };
     
   } // namespace internal
diff --git a/Filtered_kernel/examples/Filtered_kernel/Cartesian_I.h b/Filtered_kernel/examples/Filtered_kernel/Cartesian_I.h
index 06899ea1bd0..be5e4821f2e 100644
--- a/Filtered_kernel/examples/Filtered_kernel/Cartesian_I.h
+++ b/Filtered_kernel/examples/Filtered_kernel/Cartesian_I.h
@@ -93,7 +93,8 @@ struct Cartesian_base_ref_count_I
   		 intersect_with_iterators_2_object)
 #include <CGAL/Kernel/interface_macros.h>
 
-
+    template<typename A, typename B>
+    struct Intersection_result : CGAL::Intersection_traits<K, A, B> {};
 };
 
 template < typename FT_ >
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
index 6fc61d70e98..9bc233e2320 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Homogeneous_base.h
@@ -156,6 +156,8 @@ struct Homogeneous_base
 
 #include <CGAL/Kernel/interface_macros.h>
 
+    template<typename A, typename B>
+    struct Intersection_result : CGAL::Intersection_traits<Kernel, A, B> {};
 };
 
 } //namespace CGAL
diff --git a/Kernel_23/doc_tex/Kernel_23/predicates_constructions.tex b/Kernel_23/doc_tex/Kernel_23/predicates_constructions.tex
index eb076e26ff1..fec99377315 100644
--- a/Kernel_23/doc_tex/Kernel_23/predicates_constructions.tex
+++ b/Kernel_23/doc_tex/Kernel_23/predicates_constructions.tex
@@ -66,12 +66,12 @@ especially integer types and rationals.
 Some functions can return different types of objects. To achieve this
 in a type safe way {\cgal} uses return values of
 \ccStyle{boost::optional< boost::variant< T \ldots\ >} were
-T\textellipsis\ is a list of all possible resulting geometric objects.
+T... is a list of all possible resulting geometric objects.
 The exact result type of an intersection can be determined by using the
-\ccStyle{Intersection_traits} class.
+metafunction \ccc{Kernel::Intersection_result<A, B>}.
 
 \ccExample
-In the following example, the traits class is used to provide the return value for the 
+In the following example, the metafunction is used to provide the return value for the 
 \ccHtmlNoLinksFrom{intersection} computation:
 
 \ccHtmlLinksOff%
@@ -85,8 +85,7 @@ In the following example, the traits class is used to provide the return value f
 
     std::cin >> segment_1 >> segment_2;
  
-    /* IT is an alias for Intersection_traits */
-    IT< K, Segment_2, Segment_2>::result_type 
+    K::Intersection_result<Segment_2, Segment_2>::result_type 
       v = intersection(s1, s2);
     if(v) {
       /* not empty */
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Filtered_predicate.tex b/Kernel_23/doc_tex/Kernel_23_ref/Filtered_predicate.tex
index 497c196caae..3f2804f44ee 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Filtered_predicate.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Filtered_predicate.tex
@@ -53,6 +53,6 @@ It uses the fast but inexact predicate based on interval arithmetic for
 filtering and the slow but exact predicate based on multi-precision floats
 when the filtering predicate fails.
 
-\ccIncludeExampleCode{Filtered_kernel/Filtered_predicate.cpp}
+%% \ccIncludeExampleCode{Filtered_kernel/Filtered_predicate.cpp}
 
 \end{ccRefClass}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel.tex
index 0ce9097582a..e2a7d662ecc 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel.tex
@@ -52,6 +52,8 @@ number type is used such as within the filtering kernels, in which case it is
 \ccNestedType{Bounded_side}{\ccc{CGAL::Bounded_side} or \ccc{Uncertain<CGAL::Bounded_side>}}
 \ccGlue
 \ccNestedType{Angle}{\ccc{CGAL::Angle} or \ccc{Uncertain<CGAL::Angle>}}
+\ccGlue
+\ccNestedType{Intersection_result}{a model of \ccc{Kernel::Intersection_result}}
 
 \ccConstants
 
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_2.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_2.tex
index 215411a6859..1db607afeff 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_2.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_2.tex
@@ -3,18 +3,18 @@ A model for this must provide
 
 \ccCreationVariable{fo}
 
-\ccMemberFunction{Intersection_traits<K, Type1<K>, Type2<K>>::result_type operator()(Type1 obj1, Type2 obj2);}
+\ccMemberFunction{Kernel::Intersection_result<Type1, Type2>::result_type operator()(Type1 obj1, Type2 obj2);}
 {computes the \ccHtmlNoLinksFrom{intersection} region of two geometrical objects of type 
 \ccStyle{Type1} and \ccStyle{Type2}}
 
-The function is only defined for \ccStyle{Type} and \ccStyle{Type2}
-when \ccStyle{Intersection_traits<Kernel, Kernel::Type1,
-  Kernel::Type2>::result_type} is also defined.
+The function is only defined for \ccStyle{Type1} and \ccStyle{Type2}
+when \ccStyle{Kernel::Intersection_result<Type1, Type2>::result_type} is also defined.
 
 \ccRefines
 \ccc{AdaptableFunctor} (with two arguments)
 
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::intersection}\\
+\ccRefIdfierPage{CGAL::Kernel::Intersection_result<A, B>}\\
 
 \end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_3.tex b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_3.tex
index 519a08aa2d6..ce6a91378b3 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_3.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/Kernel_Intersect_3.tex
@@ -3,19 +3,18 @@ A model for this must provide
 
 \ccCreationVariable{fo}
 
-\ccMemberFunction{Intersection_traits<K, Type1<K>, Type2<K>>::result_type operator()(Type1 obj1, Type2 obj2);}
-{computes the \ccHtmlNoLinksFrom{intersection} region of two geometrical 
-objects of type \ccStyle{Type1} and \ccStyle{Type2}}
+\ccMemberFunction{Kernel::Intersection_result<Type1, Type2>::result_type operator()(Type1 obj1, Type2 obj2);}
+{computes the \ccHtmlNoLinksFrom{intersection} region of two geometrical objects of type 
+\ccStyle{Type1} and \ccStyle{Type2}}
 
-The function is only defined for \ccStyle{Type} and \ccStyle{Type2}
-when \ccStyle{Intersection_traits<Kernel, Kernel::Type1,
-  Kernel::Type2>::result_type} is also defined.
+The function is only defined for \ccStyle{Type1} and \ccStyle{Type2}
+when \ccStyle{Kernel::Intersection_result<Type1, Type2>::result_type} is also defined.
 
 \ccRefines
 \ccc{AdaptableFunctor} (with two or three arguments)
 
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::intersection}\\
-\ccRefIdfierPage{CGAL::Intersection_traits<K, A<K>, B<K>>}\\
+\ccRefIdfierPage{CGAL::Kernel::Intersection_result<A, B>}\\
 
 \end{ccRefFunctionObjectConcept}
diff --git a/Kernel_23/doc_tex/Kernel_23_ref/intersection.tex b/Kernel_23/doc_tex/Kernel_23_ref/intersection.tex
index fe7ce2f8322..604ac53f031 100644
--- a/Kernel_23/doc_tex/Kernel_23_ref/intersection.tex
+++ b/Kernel_23/doc_tex/Kernel_23_ref/intersection.tex
@@ -8,13 +8,13 @@ described below.
 
 The \ccStyle{intersection} function used to return
 \ccStyle{CGAL::Object} but starting with {\cgal} VERSION HERE the
-return type is determined by a dedicated traits class. To preserve
-backwards compatibility \ccStyle{CGAL::Object} can be constructed from
-the new return types implicitly, but switching to the new style is
-advocated. To enable the old style without any overhead, the macro
-\ccc{CGAL_INTERSECTION_VERSION} can be defined to \ccStyle{1} before
-any {\cgal} header is included or through your particular build
-system.
+return type is determined by a metafunction defined by the kernel. To
+preserve backwards compatibility \ccStyle{CGAL::Object} can be
+constructed from the new return types implicitly, but switching to the
+new style is advocated. To enable the old style without any overhead,
+the macro \ccc{CGAL_INTERSECTION_VERSION} can be defined to
+\ccStyle{1} before any {\cgal} header is included or through your
+particular build system.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \paragraph{With the basic 2D and 3D Kernel} (see Chapter~\ref{chapter-kernel-23})
@@ -23,7 +23,7 @@ system.
 
 \ccUnchecked{
 \ccRefLabel{Kernel::intersection}
-\ccFunction{IT<Type1, Type2 >::result_type intersection(Type1 obj1, Type2 obj2);}
+\ccFunction{Kernel::Intersection_result<Type1, Type2 >::result_type intersection(Type1 obj1, Type2 obj2);}
 {Two objects \ccStyle{obj1} and \ccStyle{obj2} intersect if there is a point
 \ccStyle{p} that is part of both \ccStyle{obj1} and \ccStyle{obj2}.
 The \ccHtmlNoLinksFrom{intersection} region of those two objects is defined as the set of all
@@ -39,7 +39,7 @@ The same functionality is also available through the functors \ccc{Kernel::Inter
 The possible values for types \ccStyle{Type1} and \ccStyle{Type2} and
 the value for T\ldots in \ccStyle{boost::optional< boost::variant<
   T\ldots >} are the following and can be obtained through
-\ccc{Intersection_traits<Kernel, A<Kernel>, B<Kernel>>}:
+\ccc{Kernel::Intersection_result<A, B>}:
 
 \begin{ccTexOnly}
 \begin{longtable}[c]{|l|l|l|}
@@ -512,7 +512,7 @@ with \ccc{CGAL::Dispatch_output_iterator<V,O>}.
 
 Since both the number of intersections, if any, and their type,
 depend on the arguments, the function expects an output
-iterator on \ccc{Intersection_Traits<Kernel, Type1<Kernel>, Type2<Kernel>>}, as presented below. 
+iterator on \ccc{K::Intersection_result<Type1, Type2>}, as presented below. 
 
 \ccFunction{template < class OutputIterator >
 OutputIterator
@@ -559,7 +559,7 @@ with \ccc{CGAL::Dispatch_output_iterator<V,O>}.
 
 Since both the number of intersections, if any, and their type,
 depend on the arguments, the functions expects an output
-iterator on \ccStyle{Intersection_Traits<Kernel, Type1<Kernel>, Type2<Kernel>}, as presented below. 
+iterator on \ccStyle{Kernel::Intersection_result<Type1, Type2>}, as presented below.
 
 The \textbf{first function} is:
 
@@ -651,7 +651,7 @@ struct Intersection_visitor {
 template <class R>
 void foo(Segment_2<R> seg, Line_2<R> lin)
 {
-  ITd< R, Segment_2<R>, Line_2<R> >::result_type result = intersection(seg, lin);
+  R::template Intersection_result<Segment_2<R>, Line_2<R> >::result_type result = intersection(seg, lin);
   if(result) { boost::apply_visitor(Intersection_visitor(), *result); } 
   else { /* no intersection */ }
 }
@@ -665,6 +665,7 @@ and~\ref{chapter-spherical-kernel}.
 
 \ccSeeAlso
 \ccRefIdfierPage{CGAL::do_intersect}, \\
+\ccRefIdfierPage{CGAL::Kernel::Intersection_result<A, B>}, \\ 
 \ccRefIdfierPage{CGAL::Intersection_traits<Kernel, A<Kernel>, B<Kernel>>}, \\ 
 \ccRefIdfierPage{CGAL_INTERSECTION_VERSION}, \\
 \ccAnchor{www.boost.org/doc/libs/release/libs/optional/index.html}{boost::optional}, \\
diff --git a/Kernel_23/include/CGAL/Kernel/function_objects.h b/Kernel_23/include/CGAL/Kernel/function_objects.h
index 0a9bbd460c7..24da04a8e42 100644
--- a/Kernel_23/include/CGAL/Kernel/function_objects.h
+++ b/Kernel_23/include/CGAL/Kernel/function_objects.h
@@ -2524,7 +2524,7 @@ namespace CommonKernelFunctors {
     #if CGAL_INTERSECTION_VERSION < 2
     result_type
     #else
-    typename Intersection_traits< K, T1, T2>::result_type
+    typename K::template Intersection_result< T1, T2 >::result_type
     #endif
     operator()(const T1& t1, const T2& t2) const
     { return internal::intersection(t1, t2, K()); }
@@ -2544,7 +2544,7 @@ namespace CommonKernelFunctors {
     #if CGAL_INTERSECTION_VERSION < 2
     result_type
     #else
-    typename Intersection_traits< K, T1, T2>::result_type
+    typename K::template Intersection_result< T1, T2 >::result_type
     #endif
     operator()(const T1& t1, const T2& t2) const
     { return internal::intersection(t1, t2, K() ); }