diff --git a/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp b/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
index 7d9a1382755..65a2cd0dd58 100644
--- a/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
+++ b/BGL/test/BGL/graph_concept_Linear_cell_complex.cpp
@@ -12,9 +12,9 @@ struct Myitem
   template<class Refs>
   struct Dart_wrapper
   {
-    typedef CGAL::Dart<2, Refs > Dart;
-    typedef CGAL::Cell_attribute_with_point< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute< Refs > Face_attribute;
+    typedef CGAL::Tag_true Darts_with_id;
+    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
+    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
     typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
   };
 };
diff --git a/BGL/test/BGL/test_Prefix.h b/BGL/test/BGL/test_Prefix.h
index 705a04316f2..fb938fd157d 100644
--- a/BGL/test/BGL/test_Prefix.h
+++ b/BGL/test/BGL/test_Prefix.h
@@ -46,9 +46,9 @@ struct Myitem
   template<class Refs>
   struct Dart_wrapper
   {
-    typedef CGAL::Dart<2, Refs > Dart;
-    typedef CGAL::Cell_attribute_with_point< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute< Refs > Face_attribute;
+    typedef CGAL::Tag_true Darts_with_id;
+    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
+    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
     typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
   };
 };
diff --git a/Combinatorial_map/include/CGAL/Cell_attribute.h b/Combinatorial_map/include/CGAL/Cell_attribute.h
index fb557dec046..74af7d41eb0 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute.h
@@ -42,7 +42,7 @@ namespace CGAL {
 
   namespace internal {
 
-  template<class>
+  template<class, class>
   struct Init_id;
 
   } // end namespace internal
@@ -77,15 +77,41 @@ namespace CGAL {
     Info minfo;
   };
 
+  /// Id associated with a cell attribute
+  template <class WithId>
+  class Add_id
+  {
+  public:
+    // Required to have "internal" property maps.
+    std::size_t& id()
+    { return m_id; }
+    const std::size_t& id() const
+    { return m_id; }
+
+  protected:
+    void set_id(std::size_t id)
+    { m_id=id; }
+    
+  protected:    
+    /// id of the cell
+    std::size_t m_id;
+  };
+
+  /// If the tag WithId is false, we do not add id to cells.
+  template <>
+  class Add_id<Tag_false>
+  {};
+  
   /// Cell_attribute_without_info
   template <class Refs, class Tag=Tag_true, class OnMerge=Null_functor,
-            class OnSplit=Null_functor>
+            class OnSplit=Null_functor, class WithID=Tag_false>
   class Cell_attribute_without_info;
 
   // Cell_attribute_without_info without dart support.
-  template <class Refs, class OnMerge, class OnSplit>
+  template <class Refs, class OnMerge, class OnSplit, class WithID>
   class Cell_attribute_without_info<Refs, Tag_false,
-                                    OnMerge, OnSplit>
+                                    OnMerge, OnSplit, WithID>:
+      public Add_id<WithID>
   {
     template<unsigned int, class, class>
     friend class Combinatorial_map_storage_1;
@@ -105,7 +131,7 @@ namespace CGAL {
     template <class, class>
     friend class Concurrent_compact_container;
 
-    template<class>
+    template<class, class>
     friend struct internal::Init_id;
 
   public:
@@ -117,6 +143,7 @@ namespace CGAL {
 
     typedef OnMerge On_merge;
     typedef OnSplit On_split;
+    typedef WithID Has_id;
 
     /// operator =
     Cell_attribute_without_info&
@@ -146,14 +173,6 @@ namespace CGAL {
     bool operator!=(const Cell_attribute_without_info& other) const
     { return !operator==(other); }
 
-    // Required to have "internal" property maps.
-    // TODO better (use id only when we want to use bgl ?)
-    //             (or have an id directly in compact container ?)
-    std::size_t& id()
-    { return m_id; }
-    const std::size_t& id() const
-    { return m_id; }
-
   protected:
     /// Contructor without parameter.
     Cell_attribute_without_info(): mrefcounting(0)
@@ -176,9 +195,6 @@ namespace CGAL {
       mrefcounting-=4; // 4 because the two lowest bits are reserved for cc
     }
 
-    void set_id(std::size_t id)
-    { m_id=id; }
-
   public:
     /// Get the reference counting.
     std::size_t get_nb_refs() const
@@ -196,9 +212,6 @@ namespace CGAL {
       std::size_t mrefcounting;
       void        *vp;
     };
-
-    /// id of the dart // TODO better
-    std::size_t m_id;
   };
 
   /** Definition of cell attribute.
@@ -206,9 +219,9 @@ namespace CGAL {
    * link to a dart of the cell (when T is true).
    * The refs class must provide the type of Combinatorial_map used.
    */
-  template <class Refs, class OnMerge, class OnSplit>
+  template <class Refs, class OnMerge, class OnSplit, class WithID>
   class Cell_attribute_without_info<Refs, Tag_true,
-                                    OnMerge, OnSplit>
+                                    OnMerge, OnSplit, WithID>: public Add_id<WithID>
   {
     template<unsigned int, class, class>
     friend class Combinatorial_map_storage_1;
@@ -240,6 +253,7 @@ namespace CGAL {
 
     typedef OnMerge On_merge;
     typedef OnSplit On_split;
+    typedef WithID Has_id;
 
     /// operator =
     Cell_attribute_without_info&
@@ -270,14 +284,6 @@ namespace CGAL {
     bool operator!=(const Cell_attribute_without_info& other) const
     { return !operator==(other); }
 
-    // Required to have "internal" property maps.
-    // TODO better (use id only when we want to use bgl ?)
-    //             (or have an id directly in compact container ?)
-    std::size_t& id()
-    { return m_id; }
-    const std::size_t& id() const
-    { return m_id; }
-
   protected:
     /// Contructor without parameter.
     Cell_attribute_without_info() : mdart(Refs::null_handle),
@@ -302,9 +308,6 @@ namespace CGAL {
       --mrefcounting;
     }
 
-    void set_id(std::size_t id)
-    { m_id=id; }
-
   public:
     /// Get the reference counting.
     std::size_t get_nb_refs() const
@@ -321,23 +324,20 @@ namespace CGAL {
 
     /// Reference counting: the number of darts linked to this cell.
     std::size_t mrefcounting;
-
-    /// id of the dart // TODO better
-    std::size_t m_id;
   };
 
   /// Cell associated with an attribute, with or without info depending
   /// if Info==void.
   template <class Refs, class Info_=void, class Tag_=Tag_true,
             class OnMerge=Null_functor,
-            class OnSplit=Null_functor>
+            class OnSplit=Null_functor,
+            class WithID=Tag_false>
   class Cell_attribute;
 
   /// Specialization when Info==void.
-  template <class Refs, class Tag_,
-            class OnMerge, class OnSplit>
-  class Cell_attribute<Refs, void, Tag_, OnMerge, OnSplit> :
-    public Cell_attribute_without_info<Refs, Tag_, OnMerge, OnSplit>
+  template <class Refs, class Tag_, class OnMerge, class OnSplit, class WithID>
+  class Cell_attribute<Refs, void, Tag_, OnMerge, OnSplit, WithID> :
+    public Cell_attribute_without_info<Refs, Tag_, OnMerge, OnSplit, WithID>
   {
     template<unsigned int, class, class>
     friend class Combinatorial_map_storage_1;
@@ -374,9 +374,9 @@ namespace CGAL {
 
   /// Specialization when Info!=void.
   template <class Refs, class Info_, class Tag_,
-            class OnMerge, class OnSplit>
+            class OnMerge, class OnSplit, class WithID>
   class Cell_attribute :
-    public Cell_attribute_without_info<Refs, Tag_, OnMerge, OnSplit>,
+    public Cell_attribute_without_info<Refs, Tag_, OnMerge, OnSplit, WithID>,
     public Info_for_cell_attribute<Info_>
   {
     template<unsigned int, class, class>
@@ -398,7 +398,7 @@ 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;
@@ -425,6 +425,47 @@ namespace CGAL {
     {}
   };
 
+  // A cell attribute with an id, when Info_!=void
+  template <class Refs, class Info_=void, class Tag_=Tag_true,
+            class OnMerge=Null_functor,
+            class OnSplit=Null_functor>
+  class Cell_attribute_with_id: public Cell_attribute
+      <Refs, Info_, Tag_, OnMerge, OnSplit, Tag_true>
+  {
+    template <class, class, class, class>
+    friend class Compact_container;
+
+    template <class, class>
+    friend class Concurrent_compact_container;
+
+  protected:
+    /// Default contructor.
+    Cell_attribute_with_id()
+    {}
+
+    /// Contructor with an info in parameter.
+    Cell_attribute_with_id(const Info_& ainfo) :
+      Cell_attribute<Refs, Info_, Tag_, OnMerge, OnSplit, Tag_true>(ainfo)
+    {}
+  };
+
+  /// Specialization when Info==void.
+  template <class Refs, class Tag_, class OnMerge, class OnSplit>
+  class Cell_attribute_with_id<Refs, void, Tag_, OnMerge, OnSplit>:
+      public Cell_attribute<Refs, void, Tag_, OnMerge, OnSplit, Tag_true>
+  {
+    template <class, class, class, class>
+    friend class Compact_container;
+
+    template <class, class>
+    friend class Concurrent_compact_container;
+
+  protected:
+    /// Default contructor.
+    Cell_attribute_with_id()
+    {}
+  };
+
 } // namespace CGAL
 
 #endif // CGAL_CELL_ATTRIBUTE_H //
diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h b/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
index ca1d4d6fda3..0edc5dec58b 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_storages.h
@@ -57,16 +57,18 @@ namespace CGAL {
     typedef typename Dart_wrapper::Dart                   Dart;
 #else
     typedef typename internal::template Get_dart_info<Dart_wrapper>::type
-                                                          Dart_info;
-    typedef CGAL::Dart<d_, Self, Dart_info>               Dart;
+                                                           Dart_info;
+    typedef typename internal::template Get_darts_with_id<Dart_wrapper>::type
+                                                           Darts_with_id;
+    typedef CGAL::Dart<d_, Self, Dart_info, Darts_with_id> Dart;
 #endif
-    typedef typename Alloc_::template rebind<Dart>::other Dart_allocator;
+    typedef typename Alloc_::template rebind<Dart>::other  Dart_allocator;
 
-    typedef Compact_container<Dart, Dart_allocator>       Dart_container;
+    typedef Compact_container<Dart, Dart_allocator>        Dart_container;
 
-    typedef typename Dart_container::iterator             Dart_handle;
-    typedef typename Dart_container::const_iterator       Dart_const_handle;
-    typedef typename Dart_container::size_type            size_type;
+    typedef typename Dart_container::iterator              Dart_handle;
+    typedef typename Dart_container::const_iterator        Dart_const_handle;
+    typedef typename Dart_container::size_type             size_type;
 
     typedef CGAL::Void* Null_handle_type;
     static const Null_handle_type null_handle;
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index c9acbe3e623..f7d269ddaf4 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -46,7 +46,7 @@ namespace CGAL {
 
   namespace internal {
 
-  template<class>
+  template<class, class>
   struct Init_id;
 
   } // end namespace internal
@@ -62,8 +62,8 @@ namespace CGAL {
    * n is the dimension of the space (2 for 2D, 3 for 3D...)
    * Refs the ref class
    */
-  template <unsigned int d, typename Refs>
-  struct Dart_without_info
+  template <unsigned int d, typename Refs, class WithId>
+  struct Dart_without_info: public Add_id<WithId>
   {
   public:
     template<unsigned int, class, class>
@@ -87,11 +87,12 @@ namespace CGAL {
     template<class>
     friend struct internal::Init_id;
 
-    typedef Dart_without_info<d,Refs>        Self;
-    typedef typename Refs::Dart_handle       Dart_handle;
-    typedef typename Refs::size_type         size_type;
-    typedef typename Refs::Dart_const_handle Dart_const_handle;
-    typedef typename Refs::Helper            Helper;
+    typedef Dart_without_info<d,Refs, WithId> Self;
+    typedef typename Refs::Dart_handle        Dart_handle;
+    typedef typename Refs::size_type          size_type;
+    typedef typename Refs::Dart_const_handle  Dart_const_handle;
+    typedef typename Refs::Helper             Helper;
+    typedef WithId                            Has_id;
 
     /// Typedef for attributes
     template<int i>
@@ -119,14 +120,6 @@ namespace CGAL {
       return mf[i];
     }
     
-    // Required to have "internal" property maps.
-    // TODO better (use id only when we want to use bgl ?)
-    //             (or have an id directly in compact container ?)
-    std::size_t& id()
-    { return m_id; }
-    const std::size_t& id() const
-    { return m_id; }
-
   protected:
     /** Default constructor: no real initialisation,
      *  because this is done in the combinatorial map class.
@@ -202,9 +195,6 @@ namespace CGAL {
         (mattribute_handles);
     }
 
-     void set_id(std::size_t id)
-     { m_id=id; }
-
   protected:
     /// Neighboors for each dimension +1 (from 0 to dimension).
     Dart_handle mf[dimension+1];
@@ -214,9 +204,6 @@ namespace CGAL {
 
     /// Attributes enabled
     typename Helper::Attribute_handles mattribute_handles;
-
-    /// id of the dart // TODO better
-    std::size_t m_id;
   };
 
 #if defined(CGAL_CMAP_DART_DEPRECATED) && !defined(CGAL_NO_DEPRECATED_CODE)
@@ -324,8 +311,9 @@ namespace CGAL {
 #else // CGAL_CMAP_DART_DEPRECATED
   // Dart definition with an info;
   //  (there is a specialization below when Info_==void)
-  template <unsigned int d, typename Refs, typename Info_=void>
-  struct Dart : public Dart_without_info<d, Refs>
+  template <unsigned int d, typename Refs, typename Info_=void,
+            class WithID=Tag_false>
+  struct Dart : public Dart_without_info<d, Refs, WithID>
   {
   public:
     template<unsigned int, class, class>
@@ -346,8 +334,8 @@ namespace CGAL {
     template <class, class>
     friend class Concurrent_compact_container;
 
-    typedef Dart<d, Refs, Info_> Self;
-    typedef Info_                Info;
+    typedef Dart<d, Refs, Info_, WithID> Self;
+    typedef Info_                        Info;
 
   protected:
     /** Default constructor: no real initialisation,
@@ -369,8 +357,8 @@ namespace CGAL {
   };
 
   // Specialization of Dart class when info==void
-  template <unsigned int d, typename Refs>
-  struct Dart<d, Refs, void> : public Dart_without_info<d, Refs>
+  template <unsigned int d, typename Refs, class WithID>
+  struct Dart<d, Refs, void, WithID> : public Dart_without_info<d, Refs, WithID>
   {
   public:
     typedef CGAL::Void Info;
diff --git a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
index a2a3036156e..b41369d4216 100644
--- a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
+++ b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_internal_functors.h
@@ -1037,7 +1037,8 @@ struct Beta_functor_static<CMap, Dart_handle, B, Betas...>
 };
 #endif //CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
 // ****************************************************************************
-template<typename Container>
+template<typename Container, class WitdId=
+         typename Container::value_type::Has_id>
 struct Init_id
 {
   static void run(Container& c, typename Container::iterator e)
@@ -1045,6 +1046,12 @@ struct Init_id
     e->set_id(c.index(e));
   }
 };
+template<typename Container>
+struct Init_id<Container, Tag_false>
+{
+  static void run(Container&, typename Container::iterator)
+  {}
+};
 // ****************************************************************************
 } // namespace internal
 } // namespace CGAL
diff --git a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_utility.h b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_utility.h
index d9ff3fa3cf9..beb83990d73 100644
--- a/Combinatorial_map/include/CGAL/internal/Combinatorial_map_utility.h
+++ b/Combinatorial_map/include/CGAL/internal/Combinatorial_map_utility.h
@@ -60,6 +60,16 @@ namespace CGAL
     struct Get_dart_info<T, true>
     { typedef typename Convert_void<typename T::Dart_info>::type type; };
 
+    // Get the type Darts_with_id as inner type of T.
+    // If T::Darts_with_id is not defined or if T::Darts_widh_id is Tag_false
+    BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(Has_darts_with_id,Darts_with_id,false)
+    template<typename T, bool typedefined=Has_darts_with_id<T>::value >
+    struct Get_darts_with_id
+    { typedef CGAL::Tag_false type; };
+    template<typename T>
+    struct Get_darts_with_id<T, true>
+    { typedef CGAL::Tag_true type; };
+
     // Get the type Attributes defined as inner type of T.
     // If T::Attributes is not defined, defined CGAL::cpp11::tuple<> as type.
     BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(Has_attributes_tuple,Attributes,false)
diff --git a/Generalized_map/include/CGAL/Generalized_map_storages.h b/Generalized_map/include/CGAL/Generalized_map_storages.h
index 9498cde9ef2..4e682e2df74 100644
--- a/Generalized_map/include/CGAL/Generalized_map_storages.h
+++ b/Generalized_map/include/CGAL/Generalized_map_storages.h
@@ -56,7 +56,9 @@ namespace CGAL {
 
     typedef typename internal::template Get_dart_info<Dart_wrapper>::type
                                                           Dart_info;
-    typedef CGAL::Dart<d_, Self, Dart_info>               Dart;
+    typedef typename internal::template Get_darts_with_id<Dart_wrapper>::type
+                                                           Darts_with_id;
+    typedef CGAL::Dart<d_, Self, Dart_info, Darts_with_id> Dart;
 
     typedef typename Alloc_::template rebind<Dart>::other Dart_allocator;
 
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 a55a8582fbe..4b5e9109783 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
@@ -68,16 +68,18 @@ namespace CGAL {
     typedef typename Dart_wrapper::Dart                   Dart;
 #else
     typedef typename internal::template Get_dart_info<Dart_wrapper>::type
-                                                          Dart_info;
-    typedef CGAL::Dart<d_, Self, Dart_info>               Dart;
+                                                           Dart_info;
+    typedef typename internal::template Get_darts_with_id<Dart_wrapper>::type
+                                                           Darts_with_id;
+    typedef CGAL::Dart<d_, Self, Dart_info, Darts_with_id> Dart;
 #endif
-    typedef typename Alloc_::template rebind<Dart>::other Dart_allocator;
+    typedef typename Alloc_::template rebind<Dart>::other  Dart_allocator;
 
-    typedef Compact_container<Dart, Dart_allocator>       Dart_container;
+    typedef Compact_container<Dart, Dart_allocator>        Dart_container;
 
-    typedef typename Dart_container::iterator             Dart_handle;
-    typedef typename Dart_container::const_iterator       Dart_const_handle;
-    typedef typename Dart_container::size_type            size_type;
+    typedef typename Dart_container::iterator              Dart_handle;
+    typedef typename Dart_container::const_iterator        Dart_const_handle;
+    typedef typename Dart_container::size_type             size_type;
 
     typedef CGAL::Void* Null_handle_type;
     static const Null_handle_type null_handle;
diff --git a/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h b/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
index 3331133c662..2bbeb363bff 100644
--- a/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
+++ b/Linear_cell_complex/include/CGAL/Cell_attribute_with_point.h
@@ -57,10 +57,11 @@ namespace CGAL {
   /// Attribute associated with a point and an info.
   template < class LCC, class Info_=void, class Tag=Tag_true,
              class Functor_on_merge_=Null_functor,
-             class Functor_on_split_=Null_functor >
+             class Functor_on_split_=Null_functor,
+             class WithID=Tag_false >
   class Cell_attribute_with_point :
     public Cell_attribute<LCC, Info_, Tag,
-                          Functor_on_merge_, Functor_on_split_>,
+                          Functor_on_merge_, Functor_on_split_, WithID>,
     public Point_for_cell<typename LCC::Point>
   {
     template <class, class, class, class>
@@ -112,10 +113,13 @@ namespace CGAL {
   /// Attribute associated with a point and without info.
   template < class LCC, class Tag,
              class Functor_on_merge_,
-             class Functor_on_split_ >
+             class Functor_on_split_,
+             class WithID>
   class Cell_attribute_with_point<LCC, void, Tag,
-                                  Functor_on_merge_, Functor_on_split_> :
-    public Cell_attribute<LCC, void, Tag, Functor_on_merge_, Functor_on_split_>,
+                                  Functor_on_merge_, Functor_on_split_,
+                                  WithID>:
+    public Cell_attribute<LCC, void,
+                          Tag, Functor_on_merge_, Functor_on_split_, WithID>,
     public Point_for_cell<typename LCC::Point>
   {
     template <class, class, class, class>
@@ -126,7 +130,7 @@ namespace CGAL {
 
   public:
     typedef Cell_attribute<LCC, void, Tag,
-                           Functor_on_merge_, Functor_on_split_> Base1;
+                           Functor_on_merge_, Functor_on_split_, WithID> Base1;
     typedef Point_for_cell<typename LCC::Point> Base2;
 
     typedef void                            Info;
@@ -156,6 +160,63 @@ namespace CGAL {
     Cell_attribute_with_point(const Point& apoint) : Base2(apoint)
     {}
   };
+
+  // A cell attribute with point and id, when Info_!=void
+  template <class Refs, class Info_=void, class Tag_=Tag_true,
+            class OnMerge=Null_functor,
+            class OnSplit=Null_functor>
+  class Cell_attribute_with_point_and_id: public
+      Cell_attribute_with_point<Refs, Info_, Tag_, OnMerge, OnSplit, Tag_true>
+  {
+    typedef Cell_attribute_with_point
+          <Refs, Info_, Tag_, OnMerge, OnSplit, Tag_true> Base;
+    typedef typename Refs::Point Point;
+
+    template <class, class, class, class>
+    friend class Compact_container;
+
+    template <class, class>
+    friend class Concurrent_compact_container;
+
+  protected:
+    /// Default contructor.
+    Cell_attribute_with_point_and_id()
+    {}
+
+    /// Contructor with an info in parameter.
+    Cell_attribute_with_point_and_id(const Point& apoint) : Base(apoint)
+    {}
+
+    /// Contructor with a point and an attribute in parameters.
+    Cell_attribute_with_point_and_id(const Point& apoint, const Info_& ainfo) :
+      Base(apoint, ainfo)
+    {}
+  };
+
+  /// Specialization when Info==void.
+  template <class Refs, class Tag_, class OnMerge, class OnSplit>
+  class Cell_attribute_with_point_and_id<Refs, void, Tag_, OnMerge, OnSplit>:
+      public Cell_attribute_with_point<Refs, void, Tag_, OnMerge, OnSplit, Tag_true>
+  {
+    typedef Cell_attribute_with_point
+         <Refs, void, Tag_, OnMerge, OnSplit, Tag_true> Base;
+    typedef typename Refs::Point Point;
+
+    template <class, class, class, class>
+    friend class Compact_container;
+
+    template <class, class>
+    friend class Concurrent_compact_container;
+
+  protected:
+    /// Default contructor.
+    Cell_attribute_with_point_and_id()
+    {}
+
+    /// Contructor with a point in parameter.
+    Cell_attribute_with_point_and_id(const Point& apoint) : Base(apoint)
+    {}
+  };
 } // namespace CGAL
 
 #endif // CGAL_CELL_ATTRIBUTE_WITH_POINT_H //
diff --git a/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages.h b/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages.h
index ec99f027d67..54cafb2ce2f 100644
--- a/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages.h
+++ b/Linear_cell_complex/include/CGAL/GMap_linear_cell_complex_storages.h
@@ -65,16 +65,18 @@ namespace CGAL {
     typedef typename Items_::template Dart_wrapper<Self>  Dart_wrapper;
 
     typedef typename internal::template Get_dart_info<Dart_wrapper>::type
-                                                          Dart_info;
-    typedef CGAL::Dart<d_, Self, Dart_info>               Dart;
+                                                           Dart_info;
+    typedef typename internal::template Get_darts_with_id<Dart_wrapper>::type
+                                                           Darts_with_id;
+    typedef CGAL::Dart<d_, Self, Dart_info, Darts_with_id> Dart;
 
-    typedef typename Alloc_::template rebind<Dart>::other Dart_allocator;
+    typedef typename Alloc_::template rebind<Dart>::other  Dart_allocator;
 
-    typedef Compact_container<Dart, Dart_allocator>       Dart_container;
+    typedef Compact_container<Dart, Dart_allocator>        Dart_container;
 
-    typedef typename Dart_container::iterator             Dart_handle;
-    typedef typename Dart_container::const_iterator       Dart_const_handle;
-    typedef typename Dart_container::size_type            size_type;
+    typedef typename Dart_container::iterator              Dart_handle;
+    typedef typename Dart_container::const_iterator        Dart_const_handle;
+    typedef typename Dart_container::size_type             size_type;
 
     typedef CGAL::Void* Null_handle_type;
     static const Null_handle_type null_handle;
diff --git a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
index b938c43f33f..91cc3d076c9 100644
--- a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
+++ b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_linear_cell_complex.cpp
@@ -19,9 +19,9 @@ struct Myitem
   template<class Refs>
   struct Dart_wrapper
   {
-    typedef CGAL::Dart<2, Refs > Dart;
-    typedef CGAL::Cell_attribute_with_point< Refs > Vertex_attribute;
-    typedef CGAL::Cell_attribute< Refs > Face_attribute;
+    typedef CGAL::Tag_true Darts_with_id;
+    typedef CGAL::Cell_attribute_with_point_and_id< Refs > Vertex_attribute;
+    typedef CGAL::Cell_attribute_with_id< Refs > Face_attribute;
     typedef CGAL::cpp11::tuple<Vertex_attribute, void, Face_attribute> Attributes;
   };
 };