diff --git a/Intersections_3/include/CGAL/Intersection_traits_3.h b/Intersections_3/include/CGAL/Intersection_traits_3.h
index a515eb99c2e..c82307ed8b4 100644
--- a/Intersections_3/include/CGAL/Intersection_traits_3.h
+++ b/Intersections_3/include/CGAL/Intersection_traits_3.h
@@ -23,26 +23,6 @@
 
 #include <CGAL/Intersection_traits.h>
 
-namespace CGAL {
-// global intersection declarations
-#define INTERSECT_SELF ((Line_3, 3))((Plane_3, 3))((Ray_3, 3))((Segment_3, 3))((Sphere_3, 3))((Triangle_3, 3))((Iso_cuboid_3, 3))
-#define INTERSECT ((Plane_3, Line_3, 3))((Ray_3, Line_3, 3))((Segment_3, Line_3, 3))((Triangle_3, Line_3, 3))((Ray_3, Plane_3, 3)) \
-  ((Segment_3, Plane_3, 3))((Sphere_3, Plane_3, 3))((Triangle_3, Plane_3, 3))((Segment_3, Ray_3, 3)) \
-  ((Triangle_3, Ray_3, 3))((Triangle_3, Segment_3, 3))((Iso_cuboid_3, Segment_3, 3))((Iso_cuboid_3, Line_3, 3)) \
-  ((Iso_cuboid_3, Ray_3, 3))
-#define EXPAND_SELF(s, state, x) CGAL_INTERSECTION_FUNCTION_SELF( BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(2, 0, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(2, 1, x)) )
-#define EXPAND_BINARY(s, state, x) CGAL_INTERSECTION_FUNCTION( BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 0, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 1, x)), BOOST_PP_EXPAND(BOOST_PP_TUPLE_ELEM(3, 2, x)) )
-
-// BOOST_PP_SEQ_FOR_EACH(EXPAND_SELF, _, INTERSECT_SELF)
-// BOOST_PP_SEQ_FOR_EACH(EXPAND_BINARY, _, INTERSECT)
-
-#undef EXPAND_SELF
-#undef EXPAND_BINARY
-#undef INTERSECT_SELF
-#undef INTERSECT
-}
-
-
 #if !(CGAL_INTERSECTION_VERSION < 2)
 
 namespace CGAL  {
diff --git a/Kernel_d/include/CGAL/Kernel_d/function_objects.h b/Kernel_d/include/CGAL/Kernel_d/function_objects.h
index 1a88daa25f2..88545b42d4e 100644
--- a/Kernel_d/include/CGAL/Kernel_d/function_objects.h
+++ b/Kernel_d/include/CGAL/Kernel_d/function_objects.h
@@ -142,6 +142,18 @@ template<class R>
 class Intersect
 {
   public:
+    template<typename A, typename B>
+    struct Result {
+      typedef typename Intersection_traits<R, A, B>::result_type Type;
+      // Boost MPL compatibility 
+      typedef Type type;
+    };
+
+  // Solely to make the lazy kernel work
+  #if CGAL_INTERSECTION_VERSION < 2
+    typedef CGAL::Object result_type;
+  #endif
+
     template <class T1, class T2>
     typename Intersection_traits<R, T1, T2>::result_type
     operator()(const T1& t1, const T2& t2) const
diff --git a/Kernel_d/include/CGAL/intersections_d.h b/Kernel_d/include/CGAL/intersections_d.h
index 4574334310a..22a149aa6d9 100644
--- a/Kernel_d/include/CGAL/intersections_d.h
+++ b/Kernel_d/include/CGAL/intersections_d.h
@@ -26,9 +26,6 @@
 
 #include <CGAL/basic.h>
 #include <CGAL/Intersection_traits_d.h>
-#include <CGAL/Kernel_traits.h>
-#include <CGAL/Object.h>
-
 
 namespace CGAL {
 namespace internal {
@@ -358,5 +355,37 @@ inline bool do_intersect(const typename R::Hyperplane_d& h, const typename R::Se
 { return do_intersect(s,h,r); }
 
 } //namespace internal
+
+template<typename T>
+class Hyperplane_d;
+template<typename T>
+class Line_d;
+template<typename T>
+class Segment_d;
+template<typename T>
+class Ray_d;
+
+// global intersection
+CGAL_INTERSECTION_FUNCTION_SELF(Line_d, d)
+CGAL_INTERSECTION_FUNCTION_SELF(Ray_d, d)
+CGAL_INTERSECTION_FUNCTION_SELF(Segment_d, d)
+CGAL_INTERSECTION_FUNCTION(Line_d, Ray_d, d)
+CGAL_INTERSECTION_FUNCTION(Ray_d, Segment_d, d)
+CGAL_INTERSECTION_FUNCTION(Line_d, Segment_d, d)
+CGAL_INTERSECTION_FUNCTION(Line_d, Hyperplane_d, d)
+CGAL_INTERSECTION_FUNCTION(Ray_d, Hyperplane_d, d)
+CGAL_INTERSECTION_FUNCTION(Segment_d, Hyperplane_d, d)
+
+// global do_intersect
+CGAL_DO_INTERSECT_FUNCTION_SELF(Line_d, d)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Ray_d, d)
+CGAL_DO_INTERSECT_FUNCTION_SELF(Segment_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Line_d, Ray_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Line_d, Segment_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Ray_d, Segment_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Line_d, Hyperplane_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Ray_d, Hyperplane_d, d)
+CGAL_DO_INTERSECT_FUNCTION(Segment_d, Hyperplane_d, d)
+
 } //namespace CGAL
 #endif //CGAL_INTERSECTIONS_D_H