diff --git a/Combinatorial_map/include/CGAL/Cell_attribute.h b/Combinatorial_map/include/CGAL/Cell_attribute.h
index ce35d7ce44c..153c4f643a1 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute.h
@@ -131,20 +131,20 @@ namespace CGAL {
 
     /// Increment the reference counting.
     void inc_nb_refs()
-    { ++mrefcounting; }
+    { mrefcounting+=4; } // 4 because this is the 3rd bit (ie 1<<2)
 
     /// Decrement the reference counting.
     void dec_nb_refs()
     {
-      CGAL_assertion( mrefcounting>0 );
-      --mrefcounting; 
+      CGAL_assertion( mrefcounting>3 );
+      mrefcounting-=4; // 4 because this is the 3rd bit (ie 1<<2)
     }
 
+  public:
     /// Get the reference counting.
     unsigned int get_nb_refs() const
-    { return mrefcounting; }
+    { return (mrefcounting>>2); } // >>2 to ignore the 2 least significant bits
 
-  public:
     void * for_compact_container() const 
     { return vp; }
     void * & for_compact_container()       
diff --git a/Combinatorial_map/include/CGAL/Cell_iterators.h b/Combinatorial_map/include/CGAL/Cell_iterators.h
index a9a38c1e98c..fea03a3418d 100644
--- a/Combinatorial_map/include/CGAL/Cell_iterators.h
+++ b/Combinatorial_map/include/CGAL/Cell_iterators.h
@@ -112,7 +112,10 @@ namespace CGAL {
     CMap_cell_iterator(const Self& aiterator):
       Ite(aiterator),
       mcell_mark_number(aiterator.mcell_mark_number)
-    { this->mmap->share_a_mark(this->mcell_mark_number); }
+    {
+      this->mmap->share_a_mark(this->mmark_number);
+      this->mmap->share_a_mark(this->mcell_mark_number);
+    }
 
     /// Assignment operator.
     Self& operator=(const Self& aiterator)
@@ -120,6 +123,7 @@ namespace CGAL {
       if (this != &aiterator)
       {
         Ite::operator=(aiterator);
+        this->mmap->share_a_mark(this->mmark_number);
         this->mmap->share_a_mark(mcell_mark_number);
       }
       return *this;
diff --git a/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_test.cpp b/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_test.cpp
index 1d374f684c6..c358a86a963 100644
--- a/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_test.cpp
+++ b/Linear_cell_complex/test/Linear_cell_complex/Linear_cell_complex_test.cpp
@@ -32,6 +32,19 @@ struct Myitems_2
   };
 };
 
+struct Myitems_2c
+{
+  template <class LCC>
+  struct Dart_wrapper
+  {
+    typedef CGAL::Dart<2, LCC> Dart;
+
+    typedef CGAL::Cell_attribute_with_point<LCC,int,CGAL::Tag_false,Sum_functor,
+                                            Divide_by_two_functor> myattrib;
+    typedef CGAL::cpp11::tuple<myattrib, myattrib, myattrib>
+    Attributes;
+  };
+};
 struct Myitems_3
 {
   template <class LCC>
@@ -46,6 +59,20 @@ struct Myitems_3
   };
 };
 
+struct Myitems_3c
+{
+  template <class LCC>
+  struct Dart_wrapper
+  {
+    typedef CGAL::Dart<3, LCC> Dart;
+
+    typedef CGAL::Cell_attribute_with_point<LCC,int,CGAL::Tag_false,Sum_functor,
+                                            Divide_by_two_functor> myattrib;
+    typedef CGAL::cpp11::tuple<myattrib, myattrib, myattrib, myattrib>
+    Attributes;
+  };
+};
+
 struct Myitems_4
 {
   template <class LCC>
@@ -60,6 +87,19 @@ struct Myitems_4
   };
 };
 
+struct Myitems_4c
+{
+  template <class LCC>
+  struct Dart_wrapper
+  {
+    typedef CGAL::Dart<4, LCC> Dart;
+
+    typedef CGAL::Cell_attribute_with_point<LCC,int,CGAL::Tag_false,Sum_functor,
+                                            Divide_by_two_functor> myattrib;
+    typedef CGAL::cpp11::tuple<myattrib, myattrib, myattrib, myattrib,myattrib>
+    Attributes;
+  };
+};
 
 int main()
 {
@@ -95,6 +135,14 @@ int main()
     return EXIT_FAILURE;
   }
   
+  typedef CGAL::Linear_cell_complex<2,2,
+                                    CGAL::Linear_cell_complex_traits<2>,
+                                    Myitems_2c> LCC2c;
+  if ( !test_LCC_2<LCC2c>() )
+  {
+    std::cout<<" Error during Test_LCC_2<LCC2c>."<<std::endl;
+    return EXIT_FAILURE;
+  }
   typedef CGAL::Linear_cell_complex<3,3,
                                     CGAL::Linear_cell_complex_traits<3>,
                                     Myitems_3> LCC3b;
@@ -103,6 +151,15 @@ int main()
     std::cout<<" Error during Test_LCC_3<LCC3b>."<<std::endl;
     return EXIT_FAILURE;
   }
+
+  typedef CGAL::Linear_cell_complex<3,3,
+                                    CGAL::Linear_cell_complex_traits<3>,
+                                    Myitems_3c> LCC3c;
+  if ( !test_LCC_3<LCC3c>() )
+  {
+    std::cout<<" Error during Test_LCC_3<LCC3c>."<<std::endl;
+    return EXIT_FAILURE;
+  }
   
   typedef CGAL::Linear_cell_complex<4,4,
                                     CGAL::Linear_cell_complex_traits<4>,
@@ -113,6 +170,15 @@ int main()
     return EXIT_FAILURE;
   }
 
+  typedef CGAL::Linear_cell_complex<4,4,
+                                    CGAL::Linear_cell_complex_traits<4>,
+                                    Myitems_4c> LCC4c;
+  if ( !test_LCC_4<LCC4b>() )
+  {
+    std::cout<<" Error during Test_LCC_4<LCC4c>."<<std::endl;
+    return EXIT_FAILURE;
+  }
+
   std::cout<<" Success."<<std::endl;
   return EXIT_SUCCESS;
 }