diff --git a/Kernel_23/include/CGAL/Circle_2.h b/Kernel_23/include/CGAL/Circle_2.h
index c68d149207e..8f2d22a7478 100644
--- a/Kernel_23/include/CGAL/Circle_2.h
+++ b/Kernel_23/include/CGAL/Circle_2.h
@@ -64,26 +64,26 @@ public:
 
   Circle_2(const Point_2 &center, const FT &squared_radius,
 	   const Orientation &orientation)
-    : RCircle_2(typename R::Construct_circle_2()(center, squared_radius, orientation).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(center, squared_radius, orientation)) {}
 
   Circle_2(const Point_2 &center, const FT &squared_radius)
-    : RCircle_2(typename R::Construct_circle_2()(center, squared_radius, COUNTERCLOCKWISE).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(center, squared_radius, COUNTERCLOCKWISE)) {}
 
   Circle_2(const Point_2 &p, const Point_2 &q, const Point_2 &r)
-    : RCircle_2(typename R::Construct_circle_2()(p,q,r).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(p,q,r)) {}
 
   Circle_2(const Point_2 & p, const Point_2 & q,
 	   const Orientation &orientation)
-    : RCircle_2(typename R::Construct_circle_2()(p,q,orientation).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(p,q,orientation)) {}
 
   Circle_2(const Point_2 & p, const Point_2 & q)
-    : RCircle_2(typename R::Construct_circle_2()(p,q,COUNTERCLOCKWISE).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(p,q,COUNTERCLOCKWISE)) {}
 
   Circle_2(const Point_2 & center, const Orientation& orientation)
-    : RCircle_2(typename R::Construct_circle_2()(center,FT(0),orientation).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(center,FT(0),orientation)) {}
 
   Circle_2(const Point_2 & center)
-    : RCircle_2(typename R::Construct_circle_2()(center,FT(0),COUNTERCLOCKWISE).rep()) {}
+    : RCircle_2(typename R::Construct_circle_2()(center,FT(0),COUNTERCLOCKWISE)) {}
 
   typename Qualified_result_of<typename R::Construct_center_2,Circle_2>::type
   center() const
diff --git a/Kernel_23/include/CGAL/Direction_2.h b/Kernel_23/include/CGAL/Direction_2.h
index 8a097ff601e..8d2adeea00c 100644
--- a/Kernel_23/include/CGAL/Direction_2.h
+++ b/Kernel_23/include/CGAL/Direction_2.h
@@ -65,19 +65,19 @@ public:
     : RDirection_2(d) {}
 
   Direction_2(const Vector_2& v)
-    : RDirection_2(typename R::Construct_direction_2()(v).rep()) {}
+    : RDirection_2(typename R::Construct_direction_2()(v)) {}
 
   Direction_2(const Line_2& l)
-    : RDirection_2(typename R::Construct_direction_2()(l).rep()) {}
+    : RDirection_2(typename R::Construct_direction_2()(l)) {}
 
   Direction_2(const Ray_2& r)
-    : RDirection_2(typename R::Construct_direction_2()(r).rep()) {}
+    : RDirection_2(typename R::Construct_direction_2()(r)) {}
 
   Direction_2(const Segment_2& s)
-    : RDirection_2(typename R::Construct_direction_2()(s).rep()) {}
+    : RDirection_2(typename R::Construct_direction_2()(s)) {}
 
   Direction_2(const RT &x, const RT &y)
-    :  RDirection_2(typename R::Construct_direction_2()(x,y).rep()) {}
+    :  RDirection_2(typename R::Construct_direction_2()(x,y)) {}
 
   bool
   counterclockwise_in_between(const Direction_2 &d1,
diff --git a/Kernel_23/include/CGAL/Direction_3.h b/Kernel_23/include/CGAL/Direction_3.h
index 3ac2b657495..a8081db58f5 100644
--- a/Kernel_23/include/CGAL/Direction_3.h
+++ b/Kernel_23/include/CGAL/Direction_3.h
@@ -64,19 +64,19 @@ public:
     : Rep(d) {}
 
   Direction_3(const Vector_3& v)
-    : Rep(typename R::Construct_direction_3()(v).rep()) {}
+    : Rep(typename R::Construct_direction_3()(v)) {}
 
   Direction_3(const Line_3& l)
-    : Rep(typename R::Construct_direction_3()(l).rep()) {}
+    : Rep(typename R::Construct_direction_3()(l)) {}
 
   Direction_3(const Ray_3& r)
-    : Rep(typename R::Construct_direction_3()(r).rep()) {}
+    : Rep(typename R::Construct_direction_3()(r)) {}
 
   Direction_3(const Segment_3& s)
-    : Rep(typename R::Construct_direction_3()(s).rep()) {}
+    : Rep(typename R::Construct_direction_3()(s)) {}
 
   Direction_3(const RT& hx, const RT& hy, const RT& hz)
-    : Rep(typename R::Construct_direction_3()(hx, hy, hz).rep()) {}
+    : Rep(typename R::Construct_direction_3()(hx, hy, hz)) {}
 
   Direction_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Iso_cuboid_3.h b/Kernel_23/include/CGAL/Iso_cuboid_3.h
index 0e63437f8b0..e7815f89dba 100644
--- a/Kernel_23/include/CGAL/Iso_cuboid_3.h
+++ b/Kernel_23/include/CGAL/Iso_cuboid_3.h
@@ -60,27 +60,27 @@ public:
       : Rep(r) {}
 
   Iso_cuboid_3(const Point_3& p, const Point_3& q)
-   : Rep(typename R::Construct_iso_cuboid_3()(p,q).rep()) {}
+   : Rep(typename R::Construct_iso_cuboid_3()(p,q)) {}
 
   Iso_cuboid_3(const Point_3& p, const Point_3& q, int)
-   : Rep(typename R::Construct_iso_cuboid_3()(p, q, 0).rep()) {}
+   : Rep(typename R::Construct_iso_cuboid_3()(p, q, 0)) {}
 
   Iso_cuboid_3(const Point_3 &left,   const Point_3 &right,
                const Point_3 &bottom, const Point_3 &top,
                const Point_3 &far_,   const Point_3 &close)
    : Rep(typename R::Construct_iso_cuboid_3()(left, right, bottom,
-                                                    top, far_, close).rep()) {}
+                                                    top, far_, close)) {}
 
   Iso_cuboid_3(const RT& min_hx, const RT& min_hy, const RT& min_hz,
                const RT& max_hx, const RT& max_hy, const RT& max_hz, 
                const RT& hw)
    : Rep(typename R::Construct_iso_cuboid_3()(min_hx, min_hy, min_hz,
-				     max_hx, max_hy, max_hz, hw).rep()) {}
+				     max_hx, max_hy, max_hz, hw)) {}
 
   Iso_cuboid_3(const RT& min_hx, const RT& min_hy, const RT& min_hz,
                const RT& max_hx, const RT& max_hy, const RT& max_hz)
    : Rep(typename R::Construct_iso_cuboid_3()(min_hx, min_hy, min_hz,
-					     max_hx, max_hy, max_hz).rep()) {}
+					     max_hx, max_hy, max_hz)) {}
 
 // TODO FIXME : why is Qrt not working here ? 
 // TODO       : the Cartesian and Homogeneous functors should be split here
diff --git a/Kernel_23/include/CGAL/Iso_rectangle_2.h b/Kernel_23/include/CGAL/Iso_rectangle_2.h
index c1ad33a1c2e..5122481a1b0 100644
--- a/Kernel_23/include/CGAL/Iso_rectangle_2.h
+++ b/Kernel_23/include/CGAL/Iso_rectangle_2.h
@@ -62,22 +62,22 @@ public:
     : Rep(r) {}
 
   Iso_rectangle_2(const Point_2 &p, const Point_2 &q, int)
-    : Rep(typename R::Construct_iso_rectangle_2()(p, q, 0).rep()) {}
+    : Rep(typename R::Construct_iso_rectangle_2()(p, q, 0)) {}
 
   Iso_rectangle_2(const Point_2 &p, const Point_2 &q)
-    : Rep(typename R::Construct_iso_rectangle_2()(p, q).rep()) {}
+    : Rep(typename R::Construct_iso_rectangle_2()(p, q)) {}
 
   Iso_rectangle_2(const Point_2 &left, const Point_2 &right,
                   const Point_2 &bottom, const Point_2 &top)
-    : Rep(typename R::Construct_iso_rectangle_2()(left, right, bottom, top).rep()) {}
+    : Rep(typename R::Construct_iso_rectangle_2()(left, right, bottom, top)) {}
 
   Iso_rectangle_2(const RT& min_hx, const RT& min_hy,
                   const RT& max_hx, const RT& max_hy)
-    : Rep(typename R::Construct_iso_rectangle_2()(min_hx, min_hy, max_hx, max_hy).rep()) {}
+    : Rep(typename R::Construct_iso_rectangle_2()(min_hx, min_hy, max_hx, max_hy)) {}
 
   Iso_rectangle_2(const RT& min_hx, const RT& min_hy,
                   const RT& max_hx, const RT& max_hy, const RT& hw)
-    : Rep(typename R::Construct_iso_rectangle_2()(min_hx, min_hy, max_hx, max_hy, hw).rep()) {}
+    : Rep(typename R::Construct_iso_rectangle_2()(min_hx, min_hy, max_hx, max_hy, hw)) {}
 
 
   typename Qualified_result_of<typename R::Construct_min_vertex_2, Iso_rectangle_2 >::type
diff --git a/Kernel_23/include/CGAL/Line_2.h b/Kernel_23/include/CGAL/Line_2.h
index f450a989645..b9e4031aea4 100644
--- a/Kernel_23/include/CGAL/Line_2.h
+++ b/Kernel_23/include/CGAL/Line_2.h
@@ -63,25 +63,25 @@ public:
   Line_2() {}
 
   Line_2(const Point_2 &p, const Point_2 &q)
-    : RLine_2(typename R::Construct_line_2()(p,q).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(p,q)) {}
 
   Line_2(const RT &a, const RT &b, const RT &c)
-    : RLine_2(typename R::Construct_line_2()(a,b,c).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(a,b,c)) {}
 
   Line_2(const RLine_2& l)  // conversion impl -> interface class
     : RLine_2(l) {}
 
   Line_2(const Segment_2& s)
-    : RLine_2(typename R::Construct_line_2()(s).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(s)) {}
 
   Line_2(const Ray_2& r)
-    : RLine_2(typename R::Construct_line_2()(r).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(r)) {}
 
   Line_2(const Point_2 &p, const Direction_2 &d)
-    : RLine_2(typename R::Construct_line_2()(p,d).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(p,d)) {}
 
   Line_2(const Point_2 &p, const Vector_2 &v)
-    : RLine_2(typename R::Construct_line_2()(p,v).rep()) {}
+    : RLine_2(typename R::Construct_line_2()(p,v)) {}
 
 
   RT a() const
diff --git a/Kernel_23/include/CGAL/Line_3.h b/Kernel_23/include/CGAL/Line_3.h
index f5b617153fb..c109f0caca2 100644
--- a/Kernel_23/include/CGAL/Line_3.h
+++ b/Kernel_23/include/CGAL/Line_3.h
@@ -68,19 +68,19 @@ public:
       : Rep(l) {}
 
   Line_3(const Point_3 & p, const Point_3 & q)
-      : Rep(typename R::Construct_line_3()(p, q).rep()) {}
+      : Rep(typename R::Construct_line_3()(p, q)) {}
 
   Line_3(const Segment_3 & s)
-      : Rep(typename R::Construct_line_3()(s).rep()) {}
+      : Rep(typename R::Construct_line_3()(s)) {}
 
   Line_3(const Ray_3 & r)
-      : Rep(typename R::Construct_line_3()(r).rep()) {}
+      : Rep(typename R::Construct_line_3()(r)) {}
 
   Line_3(const Point_3 & p, const Direction_3 & d)
-      : Rep(typename R::Construct_line_3()(p, d).rep()) {}
+      : Rep(typename R::Construct_line_3()(p, d)) {}
 
   Line_3(const Point_3 & p, const Vector_3 & v)
-      : Rep(typename R::Construct_line_3()(p, v).rep()) {}
+      : Rep(typename R::Construct_line_3()(p, v)) {}
 
   Line_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Plane_3.h b/Kernel_23/include/CGAL/Plane_3.h
index 054e8e66d45..f9c527b9c4f 100644
--- a/Kernel_23/include/CGAL/Plane_3.h
+++ b/Kernel_23/include/CGAL/Plane_3.h
@@ -67,25 +67,25 @@ public:
     : Rep(p) {}
 
   Plane_3(const Point_3& p, const Point_3& q, const Point_3& r)
-    : Rep(typename R::Construct_plane_3()(p, q, r).rep()) {}
+    : Rep(typename R::Construct_plane_3()(p, q, r)) {}
 
   Plane_3(const Point_3& p, const Direction_3& d)
-    : Rep(typename R::Construct_plane_3()(p, d).rep()) {}
+    : Rep(typename R::Construct_plane_3()(p, d)) {}
 
   Plane_3(const Point_3& p, const Vector_3& v)
-    : Rep(typename R::Construct_plane_3()(p, v).rep()) {}
+    : Rep(typename R::Construct_plane_3()(p, v)) {}
 
   Plane_3(const RT& a, const RT& b, const RT& c, const RT& d)
-    : Rep(typename R::Construct_plane_3()(a, b, c, d).rep()) {}
+    : Rep(typename R::Construct_plane_3()(a, b, c, d)) {}
 
   Plane_3(const Line_3& l, const Point_3& p)
-    : Rep(typename R::Construct_plane_3()(l, p).rep()) {}
+    : Rep(typename R::Construct_plane_3()(l, p)) {}
 
   Plane_3(const Segment_3& s, const Point_3& p)
-    : Rep(typename R::Construct_plane_3()(s, p).rep()) {}
+    : Rep(typename R::Construct_plane_3()(s, p)) {}
 
   Plane_3(const Ray_3& r, const Point_3& p)
-    : Rep(typename R::Construct_plane_3()(r, p).rep()) {}
+    : Rep(typename R::Construct_plane_3()(r, p)) {}
 
   Plane_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Point_2.h b/Kernel_23/include/CGAL/Point_2.h
index 00e3ca2a2e2..6fc0147e5a6 100644
--- a/Kernel_23/include/CGAL/Point_2.h
+++ b/Kernel_23/include/CGAL/Point_2.h
@@ -62,7 +62,7 @@ public:
   Point_2() {}
 
   Point_2(const Origin& o)
-    : RPoint_2(typename R::Construct_point_2()(o).rep())
+    : RPoint_2(typename R::Construct_point_2()(o))
   {}
 
 #if 1 // still needed by Min_ellipse_2...
@@ -73,11 +73,11 @@ public:
 
   template < typename T1, typename T2 >
   Point_2(const T1 &x, const T2 &y)
-    : Rep(typename R::Construct_point_2()(x, y).rep())
+    : Rep(typename R::Construct_point_2()(x, y))
   {}
 
   Point_2(const RT& hx, const RT& hy, const RT& hw)
-    : RPoint_2(typename R::Construct_point_2()(hx, hy, hw).rep())
+    : RPoint_2(typename R::Construct_point_2()(hx, hy, hw))
   {}
 
   typename Qualified_result_of<typename R::Compute_x_2,Point_2>::type
diff --git a/Kernel_23/include/CGAL/Point_3.h b/Kernel_23/include/CGAL/Point_3.h
index 0e024f448fe..441afe4c599 100644
--- a/Kernel_23/include/CGAL/Point_3.h
+++ b/Kernel_23/include/CGAL/Point_3.h
@@ -62,7 +62,7 @@ public:
   Point_3() {}
 
   Point_3(const Origin& o)
-    : Rep(typename R::Construct_point_3()(o).rep())
+    : Rep(typename R::Construct_point_3()(o))
   {}
 
 #if 1
@@ -72,11 +72,11 @@ public:
 
   template < typename T1, typename T2, typename T3 >
   Point_3(const T1& x, const T2& y, const T3& z)
-    : Rep(typename R::Construct_point_3()(x, y, z).rep())
+    : Rep(typename R::Construct_point_3()(x, y, z))
   {}
 
   Point_3(const RT& hx, const RT& hy, const RT& hz, const RT& hw)
-    : Rep(typename R::Construct_point_3()(hx, hy, hz, hw).rep())
+    : Rep(typename R::Construct_point_3()(hx, hy, hz, hw))
   {}
 
   typename Qualified_result_of<typename R::Compute_x_3, Point_3>::type
diff --git a/Kernel_23/include/CGAL/Ray_2.h b/Kernel_23/include/CGAL/Ray_2.h
index 391f795eb0b..da3659b7c15 100644
--- a/Kernel_23/include/CGAL/Ray_2.h
+++ b/Kernel_23/include/CGAL/Ray_2.h
@@ -67,16 +67,16 @@ public:
     : RRay_2(r) {}
 
   Ray_2(const Point_2 &sp, const Point_2 &secondp)
-    : RRay_2(typename R::Construct_ray_2()(sp, secondp).rep()) {}
+    : RRay_2(typename R::Construct_ray_2()(sp, secondp)) {}
 
   Ray_2(const Point_2 &sp, const Direction_2 &d)
-    : RRay_2(typename R::Construct_ray_2()(sp, d).rep()) {}
+    : RRay_2(typename R::Construct_ray_2()(sp, d)) {}
 
   Ray_2(const Point_2 &sp, const Vector_2 &v)
-    : RRay_2(typename R::Construct_ray_2()(sp, v).rep()) {}
+    : RRay_2(typename R::Construct_ray_2()(sp, v)) {}
 
   Ray_2(const Point_2 &sp, const Line_2 &l)
-    : RRay_2(typename R::Construct_ray_2()(sp, l).rep()) {}
+    : RRay_2(typename R::Construct_ray_2()(sp, l)) {}
 
 
   typename Qualified_result_of<typename R_::Construct_source_2, Ray_2>::type
diff --git a/Kernel_23/include/CGAL/Ray_3.h b/Kernel_23/include/CGAL/Ray_3.h
index 16039a46d9f..de30ce12e6c 100644
--- a/Kernel_23/include/CGAL/Ray_3.h
+++ b/Kernel_23/include/CGAL/Ray_3.h
@@ -64,16 +64,16 @@ public:
     : Rep(r) {}
 
   Ray_3(const Point_3& sp, const Point_3& secondp)
-    : Rep(typename R::Construct_ray_3()(sp, secondp).rep()) {}
+    : Rep(typename R::Construct_ray_3()(sp, secondp)) {}
 
   Ray_3(const Point_3& sp, const Vector_3& v)
-    : Rep(typename R::Construct_ray_3()(sp, v).rep()) {}
+    : Rep(typename R::Construct_ray_3()(sp, v)) {}
 
   Ray_3(const Point_3& sp, const Direction_3& d)
-    : Rep(typename R::Construct_ray_3()(sp, d).rep()) {}
+    : Rep(typename R::Construct_ray_3()(sp, d)) {}
 
   Ray_3(const Point_3& sp, const Line_3& l)
-    : Rep(typename R::Construct_ray_3()(sp, l).rep()) {}
+    : Rep(typename R::Construct_ray_3()(sp, l)) {}
 
   Ray_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Segment_2.h b/Kernel_23/include/CGAL/Segment_2.h
index e855cde82c1..655ab49e3a5 100644
--- a/Kernel_23/include/CGAL/Segment_2.h
+++ b/Kernel_23/include/CGAL/Segment_2.h
@@ -63,7 +63,7 @@ public:
   Segment_2() {}
 
   Segment_2(const Point_2 &sp, const Point_2 &ep)
-    :  RSegment_2(typename R::Construct_segment_2()(sp,ep).rep()) {}
+    :  RSegment_2(typename R::Construct_segment_2()(sp,ep)) {}
 
   // conversion from implementation class object to interface class object
   Segment_2(const RSegment_2& s)
diff --git a/Kernel_23/include/CGAL/Segment_3.h b/Kernel_23/include/CGAL/Segment_3.h
index 3bcac333177..bea97c9a614 100644
--- a/Kernel_23/include/CGAL/Segment_3.h
+++ b/Kernel_23/include/CGAL/Segment_3.h
@@ -65,7 +65,7 @@ public:
       : Rep(s) {}
 
   Segment_3(const Point_3& sp, const Point_3& ep)
-    : Rep(typename R::Construct_segment_3()(sp, ep).rep()) {}
+    : Rep(typename R::Construct_segment_3()(sp, ep)) {}
 
 // FIXME TODO : Use Qrt here !
   //typename Qualified_result_of<typename R::Construct_source_3, Segment_3>::type
diff --git a/Kernel_23/include/CGAL/Sphere_3.h b/Kernel_23/include/CGAL/Sphere_3.h
index 129d27cbbab..819e5602d50 100644
--- a/Kernel_23/include/CGAL/Sphere_3.h
+++ b/Kernel_23/include/CGAL/Sphere_3.h
@@ -62,22 +62,22 @@ public:
 
   Sphere_3(const Point_3& p, const FT& sq_rad,
            const Orientation& o = COUNTERCLOCKWISE)
-   : Rep(typename R::Construct_sphere_3()(p, sq_rad, o).rep()) {}
+   : Rep(typename R::Construct_sphere_3()(p, sq_rad, o)) {}
 
   Sphere_3(const Point_3& p, const Point_3& q,
            const Point_3& r, const Point_3& u)
-   : Rep(typename R::Construct_sphere_3()(p, q, r, u).rep()) {}
+   : Rep(typename R::Construct_sphere_3()(p, q, r, u)) {}
 
   Sphere_3(const Point_3& p, const Point_3& q, const Point_3& r,
            const Orientation& o = COUNTERCLOCKWISE)
-   : Rep(typename R::Construct_sphere_3()(p, q, r, o).rep()) {}
+   : Rep(typename R::Construct_sphere_3()(p, q, r, o)) {}
 
   Sphere_3(const Point_3& p, const Point_3&  q,
            const Orientation& o = COUNTERCLOCKWISE)
-   : Rep(typename R::Construct_sphere_3()(p, q, o).rep()) {}
+   : Rep(typename R::Construct_sphere_3()(p, q, o)) {}
 
   Sphere_3(const Point_3& p, const Orientation& o = COUNTERCLOCKWISE)
-   : Rep(typename R::Construct_sphere_3()(p, o).rep()) {}
+   : Rep(typename R::Construct_sphere_3()(p, o)) {}
 
   Sphere_3 orthogonal_transform(const Aff_transformation_3 &t) const;
 
diff --git a/Kernel_23/include/CGAL/Tetrahedron_3.h b/Kernel_23/include/CGAL/Tetrahedron_3.h
index 03b5c352336..cf7d34ddf6f 100644
--- a/Kernel_23/include/CGAL/Tetrahedron_3.h
+++ b/Kernel_23/include/CGAL/Tetrahedron_3.h
@@ -61,7 +61,7 @@ public:
 
   Tetrahedron_3(const Point_3& p, const Point_3& q,
                 const Point_3& r, const Point_3& s)
-    : Rep(typename R::Construct_tetrahedron_3()(p, q, r, s).rep()) {}
+    : Rep(typename R::Construct_tetrahedron_3()(p, q, r, s)) {}
 
   Tetrahedron_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Triangle_2.h b/Kernel_23/include/CGAL/Triangle_2.h
index 4615d75c542..07b0daf32e6 100644
--- a/Kernel_23/include/CGAL/Triangle_2.h
+++ b/Kernel_23/include/CGAL/Triangle_2.h
@@ -62,7 +62,7 @@ public:
       : RTriangle_2(t) {}
 
   Triangle_2(const Point_2 &p, const Point_2 &q, const Point_2 &r)
-      : RTriangle_2(typename R::Construct_triangle_2()(p,q,r).rep()) {}
+      : RTriangle_2(typename R::Construct_triangle_2()(p,q,r)) {}
 
   FT
   area() const
diff --git a/Kernel_23/include/CGAL/Triangle_3.h b/Kernel_23/include/CGAL/Triangle_3.h
index 720f1589895..bfea401ca60 100644
--- a/Kernel_23/include/CGAL/Triangle_3.h
+++ b/Kernel_23/include/CGAL/Triangle_3.h
@@ -63,7 +63,7 @@ public:
       : Rep(t) {}
 
   Triangle_3(const Point_3& p, const Point_3& q, const Point_3& r)
-    : Rep(typename R::Construct_triangle_3()(p, q, r).rep()) {}
+    : Rep(typename R::Construct_triangle_3()(p, q, r)) {}
 
   Triangle_3 transform(const Aff_transformation_3 &t) const
   {
diff --git a/Kernel_23/include/CGAL/Vector_2.h b/Kernel_23/include/CGAL/Vector_2.h
index d56d5dff9de..9572da3bc5c 100644
--- a/Kernel_23/include/CGAL/Vector_2.h
+++ b/Kernel_23/include/CGAL/Vector_2.h
@@ -66,25 +66,25 @@ public:
   Vector_2() {}
 
   Vector_2(const Point_2& a, const Point_2& b)
-      : RVector_2(typename R::Construct_vector_2()(a, b).rep()) {}
+      : RVector_2(typename R::Construct_vector_2()(a, b)) {}
 
   Vector_2(const RVector_2& v) : RVector_2(v) {}
 
-  Vector_2(const Segment_2 &s) : RVector_2(typename R::Construct_vector_2()(s).rep()) {}
+  Vector_2(const Segment_2 &s) : RVector_2(typename R::Construct_vector_2()(s)) {}
 
-  Vector_2(const Ray_2 &r) : RVector_2(typename R::Construct_vector_2()(r).rep()) {}
+  Vector_2(const Ray_2 &r) : RVector_2(typename R::Construct_vector_2()(r)) {}
 
-  Vector_2(const Line_2 &l) : RVector_2(typename R::Construct_vector_2()(l).rep()) {}
+  Vector_2(const Line_2 &l) : RVector_2(typename R::Construct_vector_2()(l)) {}
 
-  Vector_2(const Null_vector &v) : RVector_2(typename R::Construct_vector_2()(v).rep()) {}
+  Vector_2(const Null_vector &v) : RVector_2(typename R::Construct_vector_2()(v)) {}
 
   template < typename T1, typename T2 >
   Vector_2(const T1 &x, const T2 &y)
-    : RVector_2(typename R::Construct_vector_2()(x,y).rep())
+    : RVector_2(typename R::Construct_vector_2()(x,y))
   {}
 
   Vector_2(const RT &x, const RT &y, const RT &w)
-    : RVector_2(typename R::Construct_vector_2()(x,y,w).rep())
+    : RVector_2(typename R::Construct_vector_2()(x,y,w))
   {}
 
 
diff --git a/Kernel_23/include/CGAL/Vector_3.h b/Kernel_23/include/CGAL/Vector_3.h
index 38d21339c56..4de646fbbde 100644
--- a/Kernel_23/include/CGAL/Vector_3.h
+++ b/Kernel_23/include/CGAL/Vector_3.h
@@ -69,26 +69,26 @@ public:
       : Rep(v) {}
 
   Vector_3(const Point_3& a, const Point_3& b)
-    : Rep(typename R::Construct_vector_3()(a, b).rep()) {}
+    : Rep(typename R::Construct_vector_3()(a, b)) {}
 
   Vector_3(const Segment_3& s)
-    : Rep(typename R::Construct_vector_3()(s).rep()) {}
+    : Rep(typename R::Construct_vector_3()(s)) {}
 
   Vector_3(const Ray_3& r)
-    : Rep(typename R::Construct_vector_3()(r).rep()) {}
+    : Rep(typename R::Construct_vector_3()(r)) {}
 
   Vector_3(const Line_3& l)
-    : Rep(typename R::Construct_vector_3()(l).rep()) {}
+    : Rep(typename R::Construct_vector_3()(l)) {}
 
   Vector_3(const Null_vector& v)
-    : Rep(typename R::Construct_vector_3()(v).rep()) {}
+    : Rep(typename R::Construct_vector_3()(v)) {}
 
   template < typename T1, typename T2, typename T3 >
   Vector_3(const T1 &x, const T2 &y, const T3 &z)
-    : Rep(typename R::Construct_vector_3()(x, y, z).rep()) {}
+    : Rep(typename R::Construct_vector_3()(x, y, z)) {}
 
   Vector_3(const RT& x, const RT& y, const RT& z, const RT& w)
-    : Rep(typename R::Construct_vector_3()(x, y, z, w).rep()) {}
+    : Rep(typename R::Construct_vector_3()(x, y, z, w)) {}
 
   Direction_3 direction() const
   {