diff --git a/Triangulation_2/examples/Triangulation_2/constrained.cpp b/Triangulation_2/examples/Triangulation_2/constrained.cpp
index 5c5f123593a..a4cc7925a3f 100644
--- a/Triangulation_2/examples/Triangulation_2/constrained.cpp
+++ b/Triangulation_2/examples/Triangulation_2/constrained.cpp
@@ -6,11 +6,8 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 
-typedef CGAL::Triangulation_vertex_base_2<K>                     Vb;
-typedef CGAL::Constrained_triangulation_face_base_2<K>           Fb;
-typedef CGAL::Triangulation_data_structure_2<Vb,Fb>              TDS;
 typedef CGAL::Exact_predicates_tag                               Itag;
-typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, Itag> CDT;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K, CGAL::Default, Itag> CDT;
 typedef CDT::Point          Point;
 
 int
diff --git a/Triangulation_2/examples/Triangulation_2/constrained_plus.cpp b/Triangulation_2/examples/Triangulation_2/constrained_plus.cpp
index 5586921c7c7..798dadadd2e 100644
--- a/Triangulation_2/examples/Triangulation_2/constrained_plus.cpp
+++ b/Triangulation_2/examples/Triangulation_2/constrained_plus.cpp
@@ -8,11 +8,8 @@
 
 typedef CGAL::Exact_predicates_exact_constructions_kernel K;
 
-typedef CGAL::Triangulation_vertex_base_2<K>              Vb;
-typedef CGAL::Constrained_triangulation_face_base_2<K>    Fb;
-typedef CGAL::Triangulation_data_structure_2<Vb,Fb>       TDS;
 typedef CGAL::Exact_intersections_tag                     Itag;
-typedef CGAL::Constrained_Delaunay_triangulation_2<K,TDS,Itag> CDT;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K,CGAL::Default,Itag> CDT;
 typedef CGAL::Constrained_triangulation_plus_2<CDT>       CDTplus;
 typedef CDTplus::Point                                    Point;
 
diff --git a/Triangulation_2/examples/Triangulation_2/polylines_triangulation.cpp b/Triangulation_2/examples/Triangulation_2/polylines_triangulation.cpp
index d68bf288be9..46d2d638db9 100644
--- a/Triangulation_2/examples/Triangulation_2/polylines_triangulation.cpp
+++ b/Triangulation_2/examples/Triangulation_2/polylines_triangulation.cpp
@@ -5,18 +5,15 @@
 
 #include <vector>
 
-typedef CGAL::Exact_predicates_exact_constructions_kernel        K;
-typedef CGAL::Polygon_2<K>                                       Polygon_2;
-typedef CGAL::Triangulation_vertex_base_2<K>                     Vb;
-typedef CGAL::Constrained_triangulation_face_base_2<K>           Fb;
-typedef CGAL::Triangulation_data_structure_2<Vb,Fb>              TDS;
-typedef CGAL::Exact_intersections_tag                            Itag;
-typedef CGAL::Constrained_Delaunay_triangulation_2<K,TDS, Itag>  CDT;
-typedef CGAL::Constrained_triangulation_plus_2<CDT>              CDTP;
+typedef CGAL::Exact_predicates_exact_constructions_kernel                 K;
+typedef CGAL::Polygon_2<K>                                                Polygon_2;
+typedef CGAL::Exact_intersections_tag                                     Itag;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K,CGAL::Default, Itag> CDT;
+typedef CGAL::Constrained_triangulation_plus_2<CDT>                       CDTP;
 
-typedef CDTP::Point                                              Point;
-typedef CDTP::Constraint_id                                      Cid;
-typedef CDTP::Vertex_handle                                      Vertex_handle;
+typedef CDTP::Point                                                       Point;
+typedef CDTP::Constraint_id                                               Cid;
+typedef CDTP::Vertex_handle                                               Vertex_handle;
 
 void 
 print(const CDTP& cdtp, Cid cid)
diff --git a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
index 752b86fc293..81e77f1c2bf 100644
--- a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
@@ -56,15 +56,16 @@ namespace CGAL {
 
 
 template <class Gt, 
-          class Tds = Triangulation_data_structure_2 <
+          class Tds_ = Triangulation_data_structure_2 <
                       Triangulation_vertex_base_2<Gt>,
 		      Constrained_triangulation_face_base_2<Gt> >,
 	  class Itag = No_intersection_tag >		
 class Constrained_Delaunay_triangulation_2
-  : public  Constrained_triangulation_2<Gt, Tds, Itag> 
+  : public  Constrained_triangulation_2<Gt, Tds_, Itag>
 {
 public:
-  typedef Constrained_triangulation_2<Gt,Tds,Itag>             Ctr;
+  typedef Constrained_triangulation_2<Gt,Tds_,Itag>            Ctr;
+  typedef typename Ctr::Tds Tds;
   typedef Constrained_Delaunay_triangulation_2<Gt,Tds,Itag>    CDt;
   typedef typename Ctr::Geom_traits      Geom_traits;
   typedef typename Ctr::Intersection_tag Intersection_tag;
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 4ffa91894a0..6cb359e16e7 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -28,7 +28,7 @@
 #include <CGAL/Triangulation_2.h> 
 #include <CGAL/Constrained_triangulation_face_base_2.h>
 #include <CGAL/iterator.h>
-
+#include <CGAL/Default.h>
 #include <CGAL/intersections.h>
 #include <CGAL/squared_distance_2.h>
 
@@ -40,16 +40,23 @@ struct Exact_predicates_tag{}; // to be used with filtered exact number
 
 
 template < class Gt, 
-           class Tds = Triangulation_data_structure_2 <
-                       Triangulation_vertex_base_2<Gt>,
-		       Constrained_triangulation_face_base_2<Gt> >, 
+           class Tds_ = Triangulation_data_structure_2 <
+                          Triangulation_vertex_base_2<Gt>,
+                          Constrained_triangulation_face_base_2<Gt> >, 
            class Itag = No_intersection_tag >
-class Constrained_triangulation_2  : public Triangulation_2<Gt,Tds>
+class Constrained_triangulation_2  
+  : public Triangulation_2<Gt,typename Default::Get< Tds_,
+                                                     Triangulation_data_structure_2 <
+                                                       Triangulation_vertex_base_2<Gt>,
+                                                       Constrained_triangulation_face_base_2<Gt> > >::type >
 {
 
 public:
+  typedef typename Default::Get<Tds_, Triangulation_data_structure_2 <
+                                        Triangulation_vertex_base_2<Gt>,
+                                        Constrained_triangulation_face_base_2<Gt> > >::type Tds;
   typedef Triangulation_2<Gt,Tds> Triangulation;
-  typedef Constrained_triangulation_2<Gt,Tds,Itag>  Constrained_triangulation;
+  typedef Constrained_triangulation_2<Gt,Tds_,Itag>  Constrained_triangulation;
   
   typedef typename Triangulation::Edge Edge;
   typedef typename Triangulation::Vertex Vertex;