diff --git a/Combinatorial_map/examples/Combinatorial_map/map_3_dynamic_onmerge.cpp b/Combinatorial_map/examples/Combinatorial_map/map_3_dynamic_onmerge.cpp
index 18ebb1c952e..147653f426b 100644
--- a/Combinatorial_map/examples/Combinatorial_map/map_3_dynamic_onmerge.cpp
+++ b/Combinatorial_map/examples/Combinatorial_map/map_3_dynamic_onmerge.cpp
@@ -9,14 +9,13 @@ struct Myitem
   template<class CMap>
   struct Dart_wrapper
   {
-    typedef CGAL::Index::Cell_attribute<CMap, double> Face_attribute; // A weight
+    typedef CGAL::Cell_attribute<CMap, double> Face_attribute; // A weight
     typedef std::tuple<void,void,Face_attribute> Attributes;
   };
 };
 
 // Definition of my combinatorial map.
-//typedef CGAL::Combinatorial_map<3,Myitem> CMap_3;
-typedef CGAL::Index::Combinatorial_map<3,Myitem> CMap_3;
+typedef CGAL::Combinatorial_map<3,Myitem> CMap_3;
 typedef CMap_3::Dart_handle               Dart_handle;
 typedef CMap_3::Attribute_type<2>::type   Face_attribute;
 
diff --git a/Combinatorial_map/include/CGAL/Cell_attribute.h b/Combinatorial_map/include/CGAL/Cell_attribute.h
index c2d44f5ba11..58254547e33 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute.h
@@ -369,7 +369,7 @@ namespace CGAL {
     friend class Concurrent_compact_container;
 
   public:
-    typedef Cell_attribute<Refs, Info_, Tag_, OnMerge, OnSplit> Self;
+    typedef Cell_attribute<Refs, Info_, Tag_, OnMerge, OnSplit, WithID> Self;
 
     typedef Tag_                             Supports_cell_dart;
     typedef typename Refs::Dart_handle       Dart_handle;
@@ -385,8 +385,7 @@ namespace CGAL {
     bool operator!=(const Self& other) const
     { return !operator==(other); }
 
-
-    // protected:
+  protected:
     /// Default contructor.
     Cell_attribute()
     {}
diff --git a/Combinatorial_map/include/CGAL/Cell_attribute_with_index.h b/Combinatorial_map/include/CGAL/Cell_attribute_with_index.h
index 3b098c6c4fc..2489aeab7c1 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute_with_index.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute_with_index.h
@@ -176,7 +176,7 @@ namespace CGAL {
     bool operator!=(const Cell_attribute_without_info& other) const
     { return !operator==(other); }
 
-    //  protected:
+  protected:
     /// Contructor without parameter.
     Cell_attribute_without_info() : mdart(Refs::null_handle),
                                     mrefcounting(0)
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map.h b/Combinatorial_map/include/CGAL/Combinatorial_map.h
index ce852285e8e..6a266a213e8 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map.h
@@ -727,7 +727,7 @@ namespace CGAL {
     }
     Dart_const_handle first_dart() const
     {
-      if (darts().begin() == darts().end()) return null_dart_handle;
+      if (darts().begin() == darts().end()) return null_handle;
       return darts().begin();
     }
 
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 f0b6aabb5d4..b2aca6dc8f4 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages_with_index.h
@@ -62,7 +62,7 @@ namespace CGAL {
     typedef typename Allocator_traits::template rebind_alloc<Dart> Dart_allocator;
 
     typedef Compact_container_with_index_2<Dart,Dart_allocator,
-    Constant_size_policy_for_cc_with_size<1024>, Index_type>
+    Multiply_by_two_policy_for_cc_with_size<64>, Index_type>
     Dart_container;
 
     // typedef unsigned int Dart_index;
@@ -83,7 +83,7 @@ namespace CGAL {
     struct Container_for_attributes : public
         Compact_container_with_index_2<T,
         typename Alloc_::template rebind<T>::other,
-        Constant_size_policy_for_cc_with_size<1024>, size_type >
+        Multiply_by_two_policy_for_cc_with_size<64>, size_type >
     {};
 
     /// Typedef for attributes
diff --git a/Combinatorial_map/include/CGAL/Compact_container_with_index_2.h b/Combinatorial_map/include/CGAL/Compact_container_with_index_2.h
index 71c683add0f..9a1858d0f58 100644
--- a/Combinatorial_map/include/CGAL/Compact_container_with_index_2.h
+++ b/Combinatorial_map/include/CGAL/Compact_container_with_index_2.h
@@ -124,8 +124,10 @@ public:
   friend class internal::CC_iterator_with_index<Self, true>;
 
   template<unsigned int first_block_size_, unsigned int block_size_increment>
-    friend struct Addition_size_policy;
+  friend struct Addition_size_policy;
   template<unsigned int k> friend struct Constant_size_policy_for_cc_with_size;
+  template<unsigned int k>
+  friend struct Multiply_by_two_policy_for_cc_with_size;
 
   explicit Compact_container_with_index_2(const Allocator &a = Allocator())
   : alloc(a)
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index 400728a714f..71dccadf745 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -30,24 +30,20 @@ namespace CGAL {
   template<unsigned int, class, class, class>
   class Combinatorial_map_storage_1;
 
-  template<unsigned int, class, class, class>
-  class Combinatorial_map_storage_2;
-
   template<unsigned int, class, class, class>
   class Generalized_map_storage_1;
 
   template<unsigned int, unsigned int, class, class, class, class>
   class CMap_linear_cell_complex_storage_1;
 
-  template<unsigned int, unsigned int, class, class, class, class>
-  class CMap_linear_cell_complex_storage_2;
-
   template<unsigned int, unsigned int, class, class, class, class>
   class GMap_linear_cell_complex_storage_1;
 
   namespace internal {
+
     template<class, class>
     struct Init_id;
+
   } // end namespace internal
 
   /** @file Dart.h
diff --git a/Combinatorial_map/include/CGAL/Generic_map_min_items.h b/Combinatorial_map/include/CGAL/Generic_map_min_items.h
index 6cfbdc940fc..c481ca223c0 100644
--- a/Combinatorial_map/include/CGAL/Generic_map_min_items.h
+++ b/Combinatorial_map/include/CGAL/Generic_map_min_items.h
@@ -30,15 +30,6 @@ namespace CGAL {
     {};
   };
 
-  namespace Index 
-  {
-  struct Generic_map_min_items
-  {
-    template < class Refs >
-    struct Dart_wrapper
-    {};
-  };
-  } // namespace Index
 } // namespace CGAL
 
 #endif // CGAL_GENERIC_MAP_MIN_ITEMS_H