diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h b/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
index 0fb312b3101..7c9a7471390 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Iso_cuboid_3.h
@@ -49,6 +49,14 @@ public:
 
   Iso_cuboidC3() {}
 
+  Iso_cuboidC3(const Point_3 &p, const Point_3 &q, int)
+    : base(p, q)
+  {
+    CGAL_kernel_assertion(p.x()<=q.x());
+    CGAL_kernel_assertion(p.y()<=q.y());
+    CGAL_kernel_assertion(p.z()<=q.z());
+  }
+
   Iso_cuboidC3(const Point_3 &p, const Point_3 &q)
   {
     Construct_point_3 construct_point_3;
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h b/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
index f04a4b98930..644fd696435 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/Iso_rectangle_2.h
@@ -46,10 +46,14 @@ public:
 
   Iso_rectangleC2() {}
 
-  Iso_rectangleC2(const Point_2 &p, const Point_2 &q)
-    : base(p,q)
-  {}
+  // Iso_rectangleC2(const Point_2 &p, const Point_2 &q)
+  //  : base(p, q) {}
 
+  Iso_rectangleC2(const Point_2 &p, const Point_2 &q, int)
+    : base(p, q)
+  {
+    CGAL_kernel_assertion(p<=q);
+  }
 
   const Point_2 & min() const
   {
diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index 38db483ee93..c0add72f6c1 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -1952,6 +1952,14 @@ namespace CartesianKernelFunctors {
     typedef Iso_rectangle_2              result_type;
     typedef Arity_tag< 2 >               Arity;
 
+    Iso_rectangle_2
+    operator()(const Point_2& p, const Point_2& q, int) const
+    {
+      CGAL_kernel_assertion(p.x()<=q.x());
+      CGAL_kernel_assertion(p.y()<=q.y());
+      return Rep(p, q, 0);
+    }
+
     Iso_rectangle_2
     operator()(const Point_2& p, const Point_2& q) const
     {
@@ -1962,7 +1970,7 @@ namespace CartesianKernelFunctors {
       else               { miny = q.y(); maxy = p.y(); }
 
       return Rep(Point_2(minx, miny),
-	         Point_2(maxx, maxy));
+	         Point_2(maxx, maxy), 0);
     }
 
     Iso_rectangle_2
@@ -1974,7 +1982,7 @@ namespace CartesianKernelFunctors {
       CGAL_kernel_assertion(!less_x(right, left));
       CGAL_kernel_assertion(!less_y(top, bottom));
       return Rep(Point_2(left.x(), bottom.y()),
-		 Point_2(right.x(), top.y()));
+		 Point_2(right.x(), top.y()), 0);
     }
 
     Iso_rectangle_2
@@ -1984,7 +1992,7 @@ namespace CartesianKernelFunctors {
       CGAL_kernel_precondition(min_hx <= max_hx);
       CGAL_kernel_precondition(min_hy <= max_hy);
       return Rep(Point_2(min_hx, min_hy),
-		 Point_2(max_hx, max_hy));
+		 Point_2(max_hx, max_hy), 0);
     }
 
     Iso_rectangle_2
@@ -1993,9 +2001,9 @@ namespace CartesianKernelFunctors {
     {
       if (hw == 1)
 	return Rep(Point_2(min_hx, min_hy),
-		   Point_2(max_hx, max_hy));
+		   Point_2(max_hx, max_hy), 0);
       return Rep(Point_2(min_hx/hw, min_hy/hw),
-		 Point_2(max_hx/hw, max_hy/hw));
+		 Point_2(max_hx/hw, max_hy/hw), 0);
     }
   };
 
diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index 11778200dae..17f4932ad07 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -247,7 +247,7 @@ public:
     operator()(const typename K1::Iso_rectangle_2 &a) const
     {
         typedef typename K2::Iso_rectangle_2  Iso_rectangle_2;
-	return Iso_rectangle_2(operator()(a.min()), operator()(a.max()));
+	return Iso_rectangle_2(operator()(a.min()), operator()(a.max()), 0);
     }
 
 
@@ -332,7 +332,7 @@ public:
     operator()(const typename K1::Iso_cuboid_3 &a) const
     {
         typedef typename K2::Iso_cuboid_3 Iso_cuboid_3;
-	return Iso_cuboid_3(operator()(a.min()), operator()(a.max()));
+	return Iso_cuboid_3(operator()(a.min()), operator()(a.max()), 0);
     }
 
     std::pair<typename K2::Point_2, typename K2::Point_2>
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
index 76b7d14d6cc..23d2528f3f7 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_cuboidH3.h
@@ -46,6 +46,14 @@ public:
 
   Iso_cuboidH3() {}
 
+  Iso_cuboidH3(const Point_3& p, const Point_3& q, int)
+    : base(p, q)
+  {
+    CGAL_kernel_assertion(p.x()<=q.x());
+    CGAL_kernel_assertion(p.y()<=q.y());
+    CGAL_kernel_assertion(p.z()<=q.z());
+  }
+
   Iso_cuboidH3(const Point_3& p, const Point_3& q);
 
   Iso_cuboidH3(const Point_3& left,   const Point_3& right,
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
index 5d7fd7623b2..ddd6251ec78 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/Iso_rectangleH2.h
@@ -17,10 +17,10 @@
 //
 // $URL$
 // $Id$
-// 
+//
 //
 // Author(s)     : Stefan Schirra
- 
+
 #ifndef CGAL_ISO_RECTANGLEH2_H
 #define CGAL_ISO_RECTANGLEH2_H
 
@@ -48,13 +48,16 @@ public:
 
   Iso_rectangleH2() {}
 
-  Iso_rectangleH2(const Point_2& p, const Point_2& q)
-    : base(p,q)
-  {}
+  Iso_rectangleH2(const Point_2& p, const Point_2& q, int)
+    : base(p, q)
+  {
+    CGAL_kernel_assertion(p.x()<=q.x());
+    CGAL_kernel_assertion(p.y()<=q.y());
+  }
 
   const Point_2 & min() const;
   const Point_2 & max() const;
-  
+
   Bounded_side bounded_side(const Point_2& p) const;
 };
 
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 7c8cd87c07a..7520be0694f 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -2520,6 +2520,14 @@ namespace HomogeneousKernelFunctors {
     typedef Iso_rectangle_2   result_type;
     typedef Arity_tag< 2 >    Arity;
 
+    Iso_rectangle_2
+    operator()(const Point_2& p, const Point_2& q, int) const
+    {
+      CGAL_kernel_assertion(p.x()<=q.x());
+      CGAL_kernel_assertion(p.y()<=q.y());
+      return Rep(p, q, 0);
+    }
+
     Iso_rectangle_2
     operator()(const Point_2& p, const Point_2& q) const
     {
@@ -2530,7 +2538,7 @@ namespace HomogeneousKernelFunctors {
       {
           if ( px_g_qx && py_g_qy )
           {
-              return Rep(q, p);
+              return Rep(q, p, 0);
           }
           else
           {
@@ -2538,17 +2546,17 @@ namespace HomogeneousKernelFunctors {
              {
                  return Rep(
                  Point_2(q.hx()*p.hw(), p.hy()*q.hw(), q.hw()*p.hw() ),
-                 Point_2(p.hx()*q.hw(), q.hy()*p.hw(), q.hw()*p.hw() ));
+                 Point_2(p.hx()*q.hw(), q.hy()*p.hw(), q.hw()*p.hw() ), 0);
              }
              if ( py_g_qy )
              {
                  return Rep(
                  Point_2(p.hx()*q.hw(), q.hy()*p.hw(), q.hw()*p.hw() ),
-                 Point_2(q.hx()*p.hw(), p.hy()*q.hw(), q.hw()*p.hw() ));
+                 Point_2(q.hx()*p.hw(), p.hy()*q.hw(), q.hw()*p.hw() ), 0);
              }
           }
       }
-      return Rep(p, q);
+      return Rep(p, q, 0);
     }
 
     Iso_rectangle_2
@@ -2564,7 +2572,7 @@ namespace HomogeneousKernelFunctors {
 			   left.hw()   * bottom.hw()),
 		   Point_2(right.hx()  * top.hw(),
 			   top.hy()    * right.hw(),
-			   right.hw()  * top.hw()));
+			   right.hw()  * top.hw()), 0);
     }
 
     Iso_rectangle_2
@@ -2574,7 +2582,7 @@ namespace HomogeneousKernelFunctors {
       CGAL_kernel_precondition(min_hx <= max_hx);
       CGAL_kernel_precondition(min_hy <= max_hy);
       return Rep(Point_2(min_hx, min_hy),
-		 Point_2(max_hx, max_hy));
+		 Point_2(max_hx, max_hy), 0);
     }
 
     Iso_rectangle_2
@@ -2582,7 +2590,7 @@ namespace HomogeneousKernelFunctors {
 	       const RT& max_hx, const RT& max_hy, const RT& hw) const
     {
 	return Rep(Point_2(min_hx, min_hy, hw),
-		   Point_2(max_hx, max_hy, hw));
+		   Point_2(max_hx, max_hy, hw), 0);
     }
   };
 
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
index b27325b9caf..876354234b6 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
@@ -157,7 +157,7 @@ public:
     operator()(const typename K1::Iso_rectangle_2 &a) const
     {
 	return k.construct_iso_rectangle_2_object()(operator()(a.min()),
-		                                    operator()(a.max()));
+		                                    operator()(a.max()), 0);
     }
 
 
@@ -239,7 +239,7 @@ public:
     operator()(const typename K1::Iso_cuboid_3 &a) const
     {
 	return k.construct_iso_cuboid_3_object()(operator()(a.min()),
-		                                 operator()(a.max()));
+		                                 operator()(a.max()), 0);
     }
 
 private:
diff --git a/Kernel_23/include/CGAL/Iso_cuboid_3.h b/Kernel_23/include/CGAL/Iso_cuboid_3.h
index c47f372b6b9..4506bfb3dab 100644
--- a/Kernel_23/include/CGAL/Iso_cuboid_3.h
+++ b/Kernel_23/include/CGAL/Iso_cuboid_3.h
@@ -55,6 +55,9 @@ public:
   Iso_cuboid_3(const Point_3& p, const Point_3& q)
    : Rep(typename R::Construct_iso_cuboid_3()(p,q).rep()) {}
 
+  Iso_cuboid_3(const Point_3& p, const Point_3& q, int)
+   : Rep(typename R::Construct_iso_cuboid_3()(p, q, 0).rep()) {}
+
   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)
diff --git a/Kernel_23/include/CGAL/Iso_rectangle_2.h b/Kernel_23/include/CGAL/Iso_rectangle_2.h
index e96306a9dd8..bb9cedbd726 100644
--- a/Kernel_23/include/CGAL/Iso_rectangle_2.h
+++ b/Kernel_23/include/CGAL/Iso_rectangle_2.h
@@ -54,8 +54,11 @@ public:
   Iso_rectangle_2(const Rep& r)
     : 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()) {}
+
   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).rep()) {}
 
   Iso_rectangle_2(const Point_2 &left, const Point_2 &right,
                   const Point_2 &bottom, const Point_2 &top)
diff --git a/Kernel_23/include/CGAL/Kernel/concept_archetype_functors.h b/Kernel_23/include/CGAL/Kernel/concept_archetype_functors.h
index 54a2f1bfdac..c109a515a57 100644
--- a/Kernel_23/include/CGAL/Kernel/concept_archetype_functors.h
+++ b/Kernel_23/include/CGAL/Kernel/concept_archetype_functors.h
@@ -1150,6 +1150,10 @@ public:
     typedef Iso_cuboid_3      result_type;
     typedef Arity_tag< 2 >    Arity;
 
+    Iso_cuboid_3
+    operator()(const Point_3&, const Point_3&, int) const
+    { return Iso_cuboid_3(); }
+
     Iso_cuboid_3
     operator()(const Point_3&, const Point_3&) const
     { return Iso_cuboid_3(); }
@@ -1170,6 +1174,10 @@ public:
     typedef Iso_rectangle_2   result_type;
     typedef Arity_tag< 2 >    Arity;
 
+    Iso_rectangle_2
+    operator()(const Point_2&, const Point_2&, int) const
+    { return Iso_rectangle_2(); }
+
     Iso_rectangle_2
     operator()(const Point_2&, const Point_2&) const
     { return Iso_rectangle_2(); }
diff --git a/Kernel_23/include/CGAL/Kernel/function_objects.h b/Kernel_23/include/CGAL/Kernel/function_objects.h
index 8dea12f371d..d0571472cd5 100644
--- a/Kernel_23/include/CGAL/Kernel/function_objects.h
+++ b/Kernel_23/include/CGAL/Kernel/function_objects.h
@@ -708,6 +708,10 @@ namespace CommonKernelFunctors {
     typedef Iso_cuboid_3      result_type;
     typedef Arity_tag< 2 >    Arity;
 
+    Iso_cuboid_3
+    operator()(const Point_3& p, const Point_3& q, int) const
+    { return Rep(p, q, 0); }
+
     Iso_cuboid_3
     operator()(const Point_3& p, const Point_3& q) const
     { return Rep(p, q); }
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_cuboid_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_cuboid_3.h
index e6b985f5dc9..966b968b1c3 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_cuboid_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_cuboid_3.h
@@ -61,6 +61,7 @@ _test_cls_iso_cuboid_3(const R& )
  CGAL::Point_3<R> p13(n4, n1, n3 );       // ( 4, 1, 3)
 
  CGAL::Iso_cuboid_3<R> r1( p1, p3);
+ CGAL::Iso_cuboid_3<R> r1_( p1, p3, 0);
  CGAL::Iso_cuboid_3<R> r2( p3, p1);
  CGAL::Iso_cuboid_3<R> r3( p2, p5);
  CGAL::Iso_cuboid_3<R> r4( p5, p2);
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_rectangle_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_rectangle_2.h
index a67da7ffb6b..1e0686f5491 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_rectangle_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_cls_iso_rectangle_2.h
@@ -55,6 +55,7 @@ _test_cls_iso_rectangle_2(const R& )
  CGAL::Point_2<R> p9(-n3, n7);        // (-3, 7)
 
  CGAL::Iso_rectangle_2<R> r1( p1, p3);
+ CGAL::Iso_rectangle_2<R> r1_( p1, p3, 0);
  CGAL::Iso_rectangle_2<R> r2( p3, p1);
  CGAL::Iso_rectangle_2<R> r3( p2, p5);
  CGAL::Iso_rectangle_2<R> r4( p5, p2);
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
index ad6cb0a806c..1f0cd11ea2e 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_2.h
@@ -174,7 +174,8 @@ test_new_2(const R& rep)
   typename R::Construct_iso_rectangle_2 construct_iso_rectangle
         = rep.construct_iso_rectangle_2_object();
   Iso_rectangle_2 rec2 = construct_iso_rectangle(p4,p5);
-  Iso_rectangle_2 rec3 = construct_iso_rectangle(p4,p4,p5,p5);
+                  rec2 = construct_iso_rectangle(p2,p3,0);
+                  rec2 = construct_iso_rectangle(p4,p4,p5,p5);
 
   typename R::Construct_object_2 construct_object 
         = rep.construct_object_2_object();
@@ -600,11 +601,10 @@ test_new_2(const R& rep)
   use(d4); use(d5);
   use(c4); use(c11);
   use(r4); use(l7); use(r5); use(v7); use(v8); use(v9);
-  use(rec3);
   use(tmp9); use(tmp10); use(tmp11); use(tmp12); use(tmp12a);
   use(tmp14); use(tmp14a); use(tmp15); use(tmp16);
   use(tmp16); use(tmp17); use(tmp19); use(tmp19a); use(tmp22a);
-  use(tmp22b); use(tmp23);
+  use(tmp22b); use(tmp22c); use(tmp23);
 
   use(tmp58);
   use(tmp57); use(tmp56); use(tmp55); use(tmp54); use(tmp53b); use(tmp53a);
diff --git a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
index 7b590919460..e3b41b57bf8 100644
--- a/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
+++ b/Kernel_23/test/Kernel_23/include/CGAL/_test_new_3.h
@@ -213,7 +213,8 @@ test_new_3(const R& rep)
   typename R::Construct_iso_cuboid_3 construct_iso_cuboid
         = rep.construct_iso_cuboid_3_object();
   Iso_cuboid_3 iso1 = construct_iso_cuboid(p3,p6);
-  Iso_cuboid_3 iso2 = construct_iso_cuboid(p3,p3,p6,p6,p4,p4);
+               iso1 = construct_iso_cuboid(p2,p3,0);
+               iso1 = construct_iso_cuboid(p3,p3,p6,p6,p4,p4);
 
   typename R::Construct_object_3 construct_object
         = rep.construct_object_3_object();
@@ -708,7 +709,7 @@ test_new_3(const R& rep)
   use(l6); use(d4); use(d5); use(d6); use(d7); use(r1);
   use(h1); use(h4); use(h5); use(h6); 
   use(sp4); use(sp5); use(sp6); use(sp7); use(sp8);
-  use(t1); use(th1); use(iso2); 
+  use(t1); use(th1);
   use(tmp3); use(tmp3a);
   use(tmp9); use(tmp14a); use(tmp5); use(tmp6);
   use(tmp7); use(tmp71); use(sp1a); use(tmp72);