diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h b/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
index fb2fa8070b2..adf7b2097f7 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
@@ -98,6 +98,17 @@ namespace CGAL {
       public Helper::template Attribute_const_range<i>
     {};
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+
+    static const Null_descriptor_type null_handle;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -117,6 +128,7 @@ namespace CGAL {
     {
       // emplace null_dart; initialized in Combinatorial_map class
       null_dart_descriptor = mnull_dart_container.emplace();
+      null_dart_handle=null_dart_descriptor;
     }
 
     void clear_storage()
@@ -435,6 +447,7 @@ namespace CGAL {
   public:
     /// Void dart. A dart d is i-free if beta_i(d)=null_dart_descriptor.
     Dart_descriptor null_dart_descriptor; // Todo Dart_const_descriptor ??
+    Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
   protected:
     /// Dart container.
@@ -452,6 +465,10 @@ namespace CGAL {
   const typename Combinatorial_map_storage_1<d_, Items_, Alloc_>::Null_descriptor_type
   Combinatorial_map_storage_1<d_, Items_, Alloc_>::null_descriptor = nullptr;
 
+  template < unsigned int d_, class Items_, class Alloc_>
+  const typename Combinatorial_map_storage_1<d_, Items_, Alloc_>::Null_descriptor_type
+  Combinatorial_map_storage_1<d_, Items_, Alloc_>::null_handle = nullptr;
+
 } // namespace CGAL
 
 #if defined(BOOST_GCC)
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
index a3ec0a0bd46..4a56fe2492c 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
@@ -65,7 +65,6 @@ namespace CGAL {
 
     typedef typename Dart_container::Index Dart_index;
 
-    // Definition of old types, for backward compatibility.
     typedef Dart_index Dart_descriptor;
     typedef Dart_index Dart_const_descriptor;
     typedef typename Dart_container::size_type size_type;
@@ -105,6 +104,15 @@ namespace CGAL {
       public Helper::template Attribute_const_range<i>
     {};
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -466,6 +474,7 @@ namespace CGAL {
   public:
     /// Void dart. A dart d is i-free if beta_i(d)=null_dart_descriptor.
     static Dart_index null_dart_descriptor; //=0;
+    static Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
   protected:
     /// Dart container.
@@ -494,6 +503,19 @@ namespace CGAL {
 #endif
               );
 
+  template<unsigned int d_, class Items_, class Alloc_>
+  typename Combinatorial_map_storage_2<d_, Items_, Alloc_>::Dart_index
+  Combinatorial_map_storage_2<d_, Items_, Alloc_>::null_dart_handle(0);
+
+  template<unsigned int d_, class Items_, class Alloc_>
+  typename Combinatorial_map_storage_2<d_, Items_, Alloc_>::Null_descriptor_type
+      Combinatorial_map_storage_2<d_, Items_, Alloc_>::
+  null_handle((std::numeric_limits<Index_type>::max)()
+#ifndef CC_INDEX3
+              /2
+#endif
+              );
+
 } // namespace CGAL
 
 #if defined(BOOST_GCC)
diff --git a/Generalized_map/include/CGAL/Generalized_map_storages.h b/Generalized_map/include/CGAL/Generalized_map_storages.h
index 7d691ebd562..f0daed8375d 100644
--- a/Generalized_map/include/CGAL/Generalized_map_storages.h
+++ b/Generalized_map/include/CGAL/Generalized_map_storages.h
@@ -98,6 +98,17 @@ namespace CGAL {
       public Helper::template Attribute_const_range<i>
     {};
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+
+    static const Null_descriptor_type null_handle;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -114,7 +125,10 @@ namespace CGAL {
 
     // Init
     void init_storage()
-    { null_dart_descriptor=nullptr; }
+    {
+      null_dart_descriptor=nullptr;
+      null_dart_handle=null_dart_descriptor;
+    }
 
     void clear_storage()
     {}
@@ -427,6 +441,7 @@ namespace CGAL {
 
   protected:
     Dart_descriptor null_dart_descriptor; // To be compatible with combinatorial map
+    Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
     /// Dart container.
     Dart_container mdarts;
diff --git a/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h b/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
index 3361e2f258e..efecbed35f4 100644
--- a/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
+++ b/Generalized_map/include/CGAL/Generalized_map_storages_with_index.h
@@ -65,7 +65,6 @@ namespace CGAL {
 
     typedef typename Dart_container::Index Dart_index;
 
-    // Definition of old types, for backward compatibility.
     typedef Dart_index Dart_descriptor;
     typedef Dart_index Dart_const_descriptor;
     typedef typename Dart_container::size_type size_type;
@@ -105,6 +104,15 @@ namespace CGAL {
       public Helper::template Attribute_const_range<i>
     {};
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -423,6 +431,7 @@ namespace CGAL {
 
   protected:
     Dart_descriptor null_dart_descriptor; // To be compatible with combinatorial map
+    Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
     /// Dart container.
     Dart_container mdarts;
@@ -441,6 +450,15 @@ namespace CGAL {
 #endif
               );
 
+  template<unsigned int d_, class Items_, class Alloc_>
+  typename Generalized_map_storage_2<d_, Items_, Alloc_>::Null_descriptor_type
+      Generalized_map_storage_2<d_, Items_, Alloc_>::
+  null_handle((std::numeric_limits<Index_type>::max)()
+#ifndef CC_INDEX3
+              /2
+#endif
+              );
+
 } // namespace CGAL
 
 #if defined(BOOST_GCC)
diff --git a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages.h b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages.h
index 63897858bf3..55fac09c132 100644
--- a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages.h
+++ b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages.h
@@ -117,6 +117,19 @@ namespace CGAL {
     typedef typename Attribute_const_range<0>::type
     Vertex_attribute_const_range;
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+    using Vertex_attribute_handle=Vertex_attribute_descriptor;
+    using Vertex_attribute_const_handle=Vertex_attribute_const_descriptor;
+
+    static const Null_descriptor_type null_handle;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -136,7 +149,8 @@ namespace CGAL {
     {
       // emplace null_dart; initialized in Combinatorial_map class
       null_dart_descriptor = mnull_dart_container.emplace();
-    }
+      null_dart_handle=null_dart_descriptor;
+   }
 
     void clear_storage()
     {
@@ -468,6 +482,7 @@ namespace CGAL {
   public:
     /// Void dart. A dart d is i-free if beta_i(d)=null_dart_descriptor.
     Dart_descriptor null_dart_descriptor; // Todo Dart_const_descriptor ??
+    Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
   protected:
     /// Dart container.
@@ -488,6 +503,13 @@ namespace CGAL {
   CMap_linear_cell_complex_storage_1<d_, ambient_dim, Traits_,
                                 Items_, Alloc_>::null_descriptor = nullptr;
 
+  template<unsigned int d_, unsigned int ambient_dim,
+           class Traits_, class Items_, class Alloc_>
+  const typename CMap_linear_cell_complex_storage_1<d_, ambient_dim, Traits_,
+                                         Items_, Alloc_>::Null_descriptor_type
+  CMap_linear_cell_complex_storage_1<d_, ambient_dim, Traits_,
+                                Items_, Alloc_>::null_handle = nullptr;
+
 } // namespace CGAL
 
 #if defined(BOOST_GCC)
diff --git a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
index f30c66e702e..76102c15b9e 100644
--- a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
+++ b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
@@ -75,7 +75,6 @@ namespace CGAL {
 
     typedef typename Dart_container::Index Dart_index;
 
-    // Definition of old types, for backward compatibility.
     typedef Dart_index Dart_descriptor;
     typedef Dart_index Dart_const_descriptor;
     typedef typename Dart_container::size_type size_type;
@@ -124,6 +123,19 @@ namespace CGAL {
     typedef typename Attribute_const_range<0>::type
     Vertex_attribute_const_range;
 
+    /// Deprecated types, keep for now for backward compatibility
+    using Dart_handle=Dart_descriptor;
+    using Dart_const_handle=Dart_const_descriptor;
+
+    template<int i>
+    using Attribute_handle=Attribute_descriptor<i>;
+    template<int i>
+    using Attribute_const_handle=Attribute_const_descriptor<i>;
+    using Vertex_attribute_handle=Vertex_attribute_descriptor;
+    using Vertex_attribute_const_handle=Vertex_attribute_const_descriptor;
+
+    static Null_descriptor_type null_handle;
+
     /// Number of marks
     static const size_type NB_MARKS = 32;
 
@@ -499,6 +511,7 @@ namespace CGAL {
   public:
     /// Void dart. A dart d is i-free if beta_i(d)=null_dart_descriptor.
     static Dart_index null_dart_descriptor; //=0;
+    static Dart_descriptor null_dart_handle; // Deprecated: kept for backward compatibility
 
   protected:
     /// Dart container.
@@ -531,6 +544,23 @@ namespace CGAL {
 #endif
               );
 
+  template<unsigned int d_,  unsigned int ambient_dim, class Traits_,
+           class Items_, class Alloc_>
+  typename CMap_linear_cell_complex_storage_2<d_, ambient_dim, Traits_, Items_, Alloc_>::
+  Dart_index CMap_linear_cell_complex_storage_2<d_, ambient_dim, Traits_, Items_, Alloc_>::
+  null_dart_handle(0);
+
+  template<unsigned int d_, unsigned int ambient_dim, class Traits_,
+           class Items_, class Alloc_>
+  typename CMap_linear_cell_complex_storage_2<d_, ambient_dim, Traits_, Items_, Alloc_>::
+  Null_descriptor_type CMap_linear_cell_complex_storage_2<d_, ambient_dim, Traits_,
+                                                      Items_, Alloc_>::
+  null_handle((std::numeric_limits<Index_type>::max)()
+#ifndef CC_INDEX3
+              /2
+#endif
+              );
+
 } // namespace CGAL
 
 #if defined(BOOST_GCC)