diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
index b7e65ad1882..ef050900371 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
@@ -25,8 +25,6 @@
 #define CGAL_CARTESIAN_POINT_2_H
 
 #include <CGAL/Origin.h>
-#include <CGAL/Handle_for.h>
-#include <CGAL/constant.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -38,16 +36,12 @@ class PointC2
   typedef typename R_::Vector_2             Vector_2;
   typedef typename R_::Point_2              Point_2;
 
-// TODO : we now have 2 layers of reference counting.
-// => maybe simply suppress the one at this level?
-  typedef Vector_2                          Rep;
-  typedef typename R_::template Handle<Rep>::type  Base;
-
-  Base base;
+  // We do not use reference counting here as it is done at the Vector_2 level.
+  Vector_2 base;
 
 public:
 
-  typedef typename Rep::Cartesian_const_iterator Cartesian_const_iterator;
+  typedef typename Vector_2::Cartesian_const_iterator Cartesian_const_iterator;
   
   typedef R_                                R;
 
@@ -64,40 +58,40 @@ public:
 
   const FT& x() const
   {
-      return get(base).x();
+      return base.x();
   }
   
   const FT& y() const
   {
-      return get(base).y();
+      return base.y();
   }
 
   const FT& hx() const
   {
-      return x();
+      return base.hx();
   }
   const FT& hy() const
   {
-      return y();
+      return base.hy();
   }
   const FT& hw() const
   {
-      return constant<FT, 1>();
+      return base.hw();
   }
 
   Cartesian_const_iterator cartesian_begin() const 
   {
-    return get(base).cartesian_begin(); 
+    return base.cartesian_begin(); 
   }
 
   Cartesian_const_iterator cartesian_end() const 
   {
-    return get(base).cartesian_end(); 
+    return base.cartesian_end(); 
   }
 
   bool operator==(const PointC2 &p) const
   {
-      return get(base) == get(p.base);
+      return base == p.base;
   }
   bool operator!=(const PointC2 &p) const
   {
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
index afdc52c2582..420527d910e 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
@@ -24,9 +24,7 @@
 #ifndef CGAL_CARTESIAN_POINT_3_H
 #define CGAL_CARTESIAN_POINT_3_H
 
-#include <CGAL/Handle_for.h>
 #include <CGAL/Origin.h>
-#include <CGAL/constant.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -38,14 +36,11 @@ class PointC3
   typedef typename R_::Point_3              Point_3;
   typedef typename R_::Aff_transformation_3 Aff_transformation_3;
 
-// TODO : we have 2 levels of ref-counting here.
-  typedef Vector_3                          Rep;
-  typedef typename R_::template Handle<Rep>::type  Base;
-
-  Base base;
+  // We do not use reference counting here as it is done at the Vector_3 level.
+  Vector_3 base;
 
 public:
-  typedef typename Rep::Cartesian_const_iterator Cartesian_const_iterator;
+  typedef typename Vector_3::Cartesian_const_iterator Cartesian_const_iterator;
   typedef R_                                R;
 
   PointC3() {}
@@ -61,32 +56,32 @@ public:
 
   const FT & x() const
   {
-      return get(base).x();
+      return base.x();
   }
   const FT & y() const
   {
-      return get(base).y();
+      return base.y();
   }
   const FT & z() const
   {
-      return get(base).z();
+      return base.z();
   }
 
   const FT & hx() const
   {
-      return x();
+      return base.hx();
   }
   const FT & hy() const
   {
-      return y();
+      return base.hy();
   }
   const FT & hz() const
   {
-      return z();
+      return base.hz();
   }
   const FT & hw() const
   {
-      return constant<FT, 1>();
+      return base.hw();
   }
 
   const FT & cartesian(int i) const;
@@ -95,17 +90,17 @@ public:
 
   Cartesian_const_iterator cartesian_begin() const 
   {
-    return get(base).cartesian_begin(); 
+    return base.cartesian_begin(); 
   }
 
   Cartesian_const_iterator cartesian_end() const 
   {
-    return get(base).cartesian_end();
+    return base.cartesian_end();
   }
 
   int dimension() const
   {
-      return get(base).dimension();
+      return base.dimension();
   }
 
   Point_3 transform(const Aff_transformation_3 &t) const
@@ -119,7 +114,7 @@ inline
 const typename PointC3<R>::FT &
 PointC3<R>::cartesian(int i) const
 {
-  return get(base).cartesian(i);
+  return base.cartesian(i);
 }
 
 template < class R >
@@ -127,7 +122,7 @@ inline
 const typename PointC3<R>::FT &
 PointC3<R>::operator[](int i) const
 {
-  return get(base)[i];
+  return base[i];
 }
 
 template < class R >
@@ -135,7 +130,7 @@ inline
 const typename PointC3<R>::FT &
 PointC3<R>::homogeneous(int i) const
 {
-  return get(base).homogeneous(i);
+  return base.homogeneous(i);
 }
 
 CGAL_END_NAMESPACE
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
index 59aabbb11bf..df8d3d9cb24 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Vector_3.h
@@ -26,6 +26,7 @@
 
 #include <CGAL/Origin.h>
 #include <CGAL/array.h>
+#include <CGAL/constant.h>
 
 CGAL_BEGIN_NAMESPACE
 
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH2.h
index 48a0aeba889..d71c03eb388 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH2.h
@@ -42,19 +42,16 @@ class PointH2
   typedef typename R_::Point_2              Point_2;
   typedef typename R_::Direction_2          Direction_2;
 
-// TODO : we have 2 levels of ref-counting here.
-  typedef Vector_2                          Rep;
-  typedef typename R_::template Handle<Rep>::type  Base;
-
   typedef Rational_traits<FT>  Rat_traits;
 
-  Base base;
+  // Reference-counting is handled in Vector_2.
+  Vector_2 base;
 
 public:
 
   typedef FT Cartesian_coordinate_type;
   typedef const RT& Homogeneous_coordinate_type;
-  typedef typename Rep::Cartesian_const_iterator Cartesian_const_iterator;
+  typedef typename Vector_2::Cartesian_const_iterator Cartesian_const_iterator;
   typedef R_                                    R;
 
     PointH2() {}
@@ -77,9 +74,9 @@ public:
     bool    operator==( const PointH2<R>& p) const;
     bool    operator!=( const PointH2<R>& p) const;
 
-    const RT & hx() const { return get(base).hx(); }
-    const RT & hy() const { return get(base).hy(); }
-    const RT & hw() const { return get(base).hw(); }
+    const RT & hx() const { return base.hx(); }
+    const RT & hy() const { return base.hy(); }
+    const RT & hw() const { return base.hw(); }
 
     FT      x()  const { return FT(hx()) / FT(hw()); }
     FT      y()  const { return FT(hy()) / FT(hw()); }
@@ -90,12 +87,12 @@ public:
 
     Cartesian_const_iterator cartesian_begin() const
     {
-      return get(base).cartesian_begin();
+      return base.cartesian_begin();
     }
 
     Cartesian_const_iterator cartesian_end() const
     {
-      return get(base).cartesian_end();
+      return base.cartesian_end();
     }
 
     int     dimension() const;
@@ -104,11 +101,11 @@ public:
 };
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 bool
 PointH2<R>::operator==( const PointH2<R>& p) const
 {
-  return get(base) == get(p.base);
+  return base == p.base;
 }
 
 template < class R >
@@ -118,36 +115,36 @@ PointH2<R>::operator!=( const PointH2<R>& p) const
 { return !(*this == p); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH2<R>::FT
 PointH2<R>::cartesian(int i) const
 {
-  return get(base).cartesian(i);
+  return base.cartesian(i);
 }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 const typename PointH2<R>::RT &
 PointH2<R>::homogeneous(int i) const
 {
-  return get(base).homogeneous(i);
+  return base.homogeneous(i);
 }
 
 template < class R >
 inline
 typename PointH2<R>::FT
 PointH2<R>::operator[](int i) const
-{ return get(base)[i]; }
+{ return base[i]; }
 
 
 template < class R >
 inline
 int
 PointH2<R>::dimension() const
-{ return get(base).dimension(); }
+{ return base.dimension(); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH2<R>::Direction_2
 PointH2<R>::direction() const
 { return typename PointH2<R>::Direction_2(*this); }
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
index df37995719b..ca966a064e9 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/PointH3.h
@@ -42,16 +42,14 @@ class PointH3
    typedef typename R_::Direction_3          Direction_3;
    typedef typename R_::Aff_transformation_3 Aff_transformation_3;
 
-   typedef Vector_3                          Rep;
-   typedef typename R_::template Handle<Rep>::type  Base;
-
    typedef Rational_traits<FT>  Rat_traits;
 
-   Base base;
+   // Reference-counting is handled in Vector_3.
+   Vector_3 base;
 
 public:
 
-   typedef typename Rep::Cartesian_const_iterator Cartesian_const_iterator;
+   typedef typename Vector_3::Cartesian_const_iterator Cartesian_const_iterator;
    typedef R_                 R;
 
   PointH3() {}
@@ -86,12 +84,12 @@ public:
 
   Cartesian_const_iterator cartesian_begin() const
   {
-    return get(base).cartesian_begin();
+    return base.cartesian_begin();
   }
 
   Cartesian_const_iterator cartesian_end() const
   {
-    return get(base).cartesian_end();
+    return base.cartesian_end();
   }
 
   int   dimension() const;
@@ -108,64 +106,64 @@ template < class R >
 inline
 const typename PointH3<R>::RT &
 PointH3<R>::hx() const
-{ return get(base).hx(); }
+{ return base.hx(); }
 
 template < class R >
 inline
 const typename PointH3<R>::RT &
 PointH3<R>::hy() const
-{ return get(base).hy(); }
+{ return base.hy(); }
 
 template < class R >
 inline
 const typename PointH3<R>::RT &
 PointH3<R>::hz() const
-{ return get(base).hz(); }
+{ return base.hz(); }
 
 template < class R >
 inline
 const typename PointH3<R>::RT &
 PointH3<R>::hw() const
-{ return get(base).hw(); }
+{ return base.hw(); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH3<R>::FT
 PointH3<R>::x()  const
-{ return FT(hx()) / FT(hw()); }
+{ return base.x(); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH3<R>::FT
 PointH3<R>::y()  const
-{ return FT(hy()) / FT(hw()); }
+{ return base.y(); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH3<R>::FT
 PointH3<R>::z()  const
-{ return FT(hz()) / FT(hw()); }
+{ return base.z(); }
 
 template < class R >
 inline
 int
 PointH3<R>::dimension() const
-{ return get(base).dimension(); }
+{ return base.dimension(); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 typename PointH3<R>::FT
 PointH3<R>::cartesian(int i) const
 {
-  return get(base).cartesian(i);
+  return base.cartesian(i);
 }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 const typename PointH3<R>::RT &
 PointH3<R>::homogeneous(int i) const
 {
-  return get(base).homogeneous(i);
+  return base.homogeneous(i);
 }
 
 template < class R >
@@ -173,7 +171,7 @@ inline
 typename PointH3<R>::FT
 PointH3<R>::operator[](int i) const
 {
-  return get(base)[i];
+  return base[i];
 }
 
 template < class R >
@@ -183,11 +181,11 @@ PointH3<R>::direction() const
 { return Direction_3(*this); }
 
 template < class R >
-CGAL_KERNEL_INLINE
+inline
 bool
 PointH3<R>::operator==( const PointH3<R> & p) const
 {
-  return get(base) == get(p.base);
+  return base == p.base;
 }
 
 template < class R >