diff --git a/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_triangulation_2.h b/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_triangulation_2.h
index 348428439f7..e9fcc57d555 100644
--- a/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_triangulation_2.h
+++ b/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_triangulation_2.h
@@ -132,9 +132,14 @@ _test_cls_triangulation_2( const Triangul & )
   assert( T1.number_of_vertices() == 0 );
 
   Triangul T3(T1);
-  Triangul T4 = T1;
-  T3.swap(T1);
+  assert(T3.tds().vertices().size() == T1.tds().vertices().size());
+  assert(T3.tds().faces().size() == T1.tds().faces().size());
 
+  Triangul T4 = T1;
+  assert(T4.tds().vertices().size() == T1.tds().vertices().size());
+  assert(T4.tds().faces().size() == T1.tds().faces().size());
+
+  T3.swap(T1);
 
   /**************************/
   /******* INSERTIONS *******/
@@ -162,6 +167,10 @@ _test_cls_triangulation_2( const Triangul & )
   assert( T0_1.number_of_faces() == 0);
   assert( T0_1.is_valid() );
 
+  Triangul T0_1b(T0_1);
+  assert(T0_1b.tds().vertices().size() == T0_1.tds().vertices().size());
+  assert(T0_1b.tds().faces().size() == T0_1.tds().faces().size());
+
   // test insert_first()
   Triangul T0_2;
   Vertex_handle v0_2_0 =   T0_2.insert_first(p0);
@@ -184,6 +193,10 @@ _test_cls_triangulation_2( const Triangul & )
   assert( T1_2.number_of_faces() == 0 );
   assert( T1_2.is_valid() );
 
+  Triangul T1_2b(T1_2);
+  assert(T1_2b.tds().vertices().size() == T1_2.tds().vertices().size());
+  assert(T1_2b.tds().faces().size() == T1_2.tds().faces().size());
+
   // p1,p3,p2  [endpoints first]
   Triangul T1_3_0;
   Vertex_handle v1_3_0_1 = T1_3_0.insert(p1); assert( v1_3_0_1 != NULL );
diff --git a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_triangulation_3.h b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_triangulation_3.h
index a2afe749131..5bca6985c83 100644
--- a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_triangulation_3.h
+++ b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_triangulation_3.h
@@ -190,7 +190,21 @@ _test_cls_triangulation_3(const Triangulation &)
   //########################################################################
 
 
-  /**************CONSTRUCTORS (1)*********************/
+  /************** CONSTRUCTORS (1)********************/
+
+  Cls Tm1;
+  assert( Tm1.dimension() == -1 );
+  assert( Tm1.number_of_vertices() == 0 );
+
+  Cls Tm3(Tm1);
+  assert(Tm3 == Tm1);
+
+  Cls Tm4 = Tm1;
+  assert(Tm4 == Tm1);
+
+  Tm3.swap(Tm1);
+
+  /************** INSERTIONS *************************/
   /************** and I/O ****************************/
 
   std::cout << "    Constructor " << std::endl;