diff --git a/Kernel_23/include/CGAL/Bbox.h b/Kernel_23/include/CGAL/Bbox.h
index fb893cc6e62..ec7b35b4314 100644
--- a/Kernel_23/include/CGAL/Bbox.h
+++ b/Kernel_23/include/CGAL/Bbox.h
@@ -19,6 +19,7 @@
 #include <iostream>
 #include <iterator>
 #include <CGAL/assertions.h>
+#include <CGAL/Dimension.h>
 
 namespace CGAL {
 namespace Impl {
@@ -122,9 +123,12 @@ protected:
 
 }
 
+template <typename Di, typename T>
+class Bbox;
+
 // A fixed D-dimensional axis aligned box
 template<unsigned int N, typename T>
-class Bbox : public Impl::Bbox<std::array<T, N>, Bbox<N,T>>
+class Bbox<Dimension_tag<N>> : public Impl::Bbox<std::array<T, N>, Bbox<N,T>>
 {
     enum { D = N };
 public:
@@ -137,7 +141,7 @@ public:
 
 // A dynamic D-dimensional axis aligned box
 template<typename T>
-class Bbox<0,T> : public Impl::Bbox<std::vector<T>, Bbox<0,T>>
+class Bbox<Dynamic_dimension_tag,T> : public Impl::Bbox<std::vector<T>, Bbox<0,T>>
 {
 public:
     inline int dimension() const { return this->min_values.size(); }
diff --git a/Kernel_23/test/Kernel_23/test_bbox.cpp b/Kernel_23/test/Kernel_23/test_bbox.cpp
index 05d519ba513..b46deff6f2e 100644
--- a/Kernel_23/test/Kernel_23/test_bbox.cpp
+++ b/Kernel_23/test/Kernel_23/test_bbox.cpp
@@ -82,7 +82,7 @@ int main()
 
   {
   //Dimension d
-  typedef CGAL::Bbox<3,double> BBox3;
+  typedef CGAL::Bbox<CGAL::Dimension_tag<3>,double> BBox3;
   BBox3 bb3(3), bb3a(3,1.0);
   assert(bb3.dimension() == 3);
   assert(bb3 != bb3a);
diff --git a/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h b/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
index 62aabe79401..c2d6b6801ba 100644
--- a/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
+++ b/NewKernel_d/include/CGAL/NewKernel_d/function_objects_cartesian.h
@@ -1010,15 +1010,16 @@ namespace CartesianDKernelFunctors {
 template<class R_> struct ConstructBbox : private Store_kernel<R_> {
         CGAL_FUNCTOR_INIT_STORE(ConstructBbox)
         typedef R_ R;
+        typedef typename R::Dimension Dimension;
         typedef typename Get_type<R, RT_tag>::type RT;
         typedef typename Get_type<R, Point_tag>::type Point;
         typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
-        typedef Bbox<DIM,double> result_type;
+        typedef Bbox<Dimension,double> result_type;
         typedef Point argument_type;
         result_type operator()(Point const&a)const{
                 CI ci(this->kernel());
                 To_interval f;
-                return result_type(DIM, make_transforming_iterator(ci(a,Begin_tag()),f), make_transforming_iterator(ci(a,End_tag())), f);
+                return result_type(a.dimension(), make_transforming_iterator(ci(a,Begin_tag()),f), make_transforming_iterator(ci(a,End_tag())), f);
         }
 };
 }