diff --git a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
index cadb269b08c..18b231feb33 100644
--- a/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
+++ b/Convex_hull_3/include/CGAL/Convex_hull_3/dual/halfspace_intersection_3.h
@@ -64,8 +64,6 @@ namespace CGAL
 
               typedef typename boost::graph_traits<Polyhedron_dual>::face_descriptor 
                 Facet_const_handle;
-              typedef typename boost::graph_traits<Polyhedron_dual>::face_iterator
-                Facet_const_iterator;
               typedef typename boost::graph_traits<Polyhedron_dual>::vertex_descriptor
                 Vertex_const_descriptor;
               typedef typename boost::graph_traits<Polyhedron_dual>::halfedge_descriptor
diff --git a/HalfedgeDS/include/CGAL/HalfedgeDS_list.h b/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
index c316a89f3ab..6bf11e83a35 100644
--- a/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
+++ b/HalfedgeDS/include/CGAL/HalfedgeDS_list.h
@@ -137,9 +137,9 @@ public:
     typedef typename Halfedge_list::const_iterator     Halfedge_const_iterator;
 
     typedef N_step_adaptor_derived<Halfedge_iterator, 2>
-                                                  Edge_iterator;
+                                                       Edge_iterator;
     typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
-                                                  Edge_const_iterator;
+                                                       Edge_const_iterator;
   
     typedef In_place_list<Face,false,Face_allocator>   Face_list;
     typedef typename Face_list::iterator               Face_handle;
diff --git a/HalfedgeDS/include/CGAL/HalfedgeDS_vector.h b/HalfedgeDS/include/CGAL/HalfedgeDS_vector.h
index d0eb33bc91e..1ae64e3b589 100644
--- a/HalfedgeDS/include/CGAL/HalfedgeDS_vector.h
+++ b/HalfedgeDS/include/CGAL/HalfedgeDS_vector.h
@@ -32,6 +32,7 @@
 #include <CGAL/basic.h>
 #include <CGAL/memory.h>
 #include <CGAL/HalfedgeDS_items_decorator.h>
+#include <CGAL/N_step_adaptor_derived.h>
 #include <algorithm>
 #include <vector>
 #include <map>
@@ -75,7 +76,7 @@ public:
     typedef typename Face_alloc_rebind::other          Face_allocator;
 
 #ifdef CGAL__HALFEDGEDS_USE_INTERNAL_VECTOR
-    typedef internal::vector<Vertex, Vertex_allocator>    Vertex_vector;
+    typedef internal::vector<Vertex, Vertex_allocator> Vertex_vector;
     typedef typename Vertex_vector::iterator           Vertex_I;
     typedef typename Vertex_vector::const_iterator     Vertex_CI;
     typedef typename Vertex_vector::iterator           Vertex_iterator;
@@ -87,7 +88,12 @@ public:
     typedef typename Halfedge_vector::iterator         Halfedge_iterator;
     typedef typename Halfedge_vector::const_iterator   Halfedge_const_iterator;
 
-    typedef internal::vector<Face, Face_allocator>        Face_vector;
+    typedef N_step_adaptor_derived<Halfedge_iterator, 2>
+                                                       Edge_iterator;
+    typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
+                                                       Edge_const_iterator;
+  
+    typedef internal::vector<Face, Face_allocator>     Face_vector;
     typedef typename Face_vector::iterator             Face_I;
     typedef typename Face_vector::const_iterator       Face_CI;
     typedef typename Face_vector::iterator             Face_iterator;
diff --git a/Point_set_processing_3/include/CGAL/Point_set_processing_3/internal/Voronoi_covariance_3/voronoi_covariance_3.h b/Point_set_processing_3/include/CGAL/Point_set_processing_3/internal/Voronoi_covariance_3/voronoi_covariance_3.h
index 1907219b70a..c1fbe4059b6 100644
--- a/Point_set_processing_3/include/CGAL/Point_set_processing_3/internal/Voronoi_covariance_3/voronoi_covariance_3.h
+++ b/Point_set_processing_3/include/CGAL/Point_set_processing_3/internal/Voronoi_covariance_3/voronoi_covariance_3.h
@@ -37,6 +37,8 @@
 #include <CGAL/Convex_hull_3/dual/halfspace_intersection_3.h>
 #endif
 
+#include <CGAL/HalfedgeDS_default.h>
+
 /// \cond SKIP_IN_MANUAL
 
 namespace CGAL {
@@ -144,7 +146,7 @@ namespace CGAL {
                     typedef typename K::Plane_3 Plane;
                     typedef typename K::Point_3 Point;
                     typedef typename K::Vector_3 Vector;
-                    typedef typename CGAL::Convex_hull_traits_3<K> Traits;
+                    typedef typename CGAL::Convex_hull_traits_3<K, HalfedgeDS_default<K,HalfedgeDS_items_3> > Traits;
                     typedef typename Traits::Polygon_mesh Polyhedron;
 
                     std::list<Vertex_handle> vertices;
@@ -176,16 +178,15 @@ namespace CGAL {
                        boost::make_optional(Point(CGAL::ORIGIN)));
 
                     // apply f to the triangles on the boundary of P
-                    for (typename Polyhedron::Facet_iterator it = P.facets_begin();
-                         it != P.facets_end(); ++it)
+                    BOOST_FOREACH(typename boost::graph_traits<Polyhedron>::face_descriptor fd, faces(P))
                     {
-                        typename Polyhedron::Halfedge_around_facet_circulator
-                            h0 = it->facet_begin(), hf = h0--, hs = cpp11::next(hf);
+                      Halfedge_around_face_circulator<Polyhedron>
+                        h0(halfedge(fd,P),P), hf = h0--, hs = cpp11::next(hf);
 
                         while(hs != h0)
                         {
-                            f (h0->vertex()->point(), hf->vertex()->point(),
-                               hs->vertex()->point());
+                          f ((*h0)->vertex()->point(), (*hf)->vertex()->point(),
+                             (*hs)->vertex()->point());
                             ++hs; ++hf;
                         }
                     }
diff --git a/Point_set_processing_3/test/Point_set_processing_3/normal_estimation_test.cpp b/Point_set_processing_3/test/Point_set_processing_3/normal_estimation_test.cpp
index 4ffa5863254..1c640709039 100644
--- a/Point_set_processing_3/test/Point_set_processing_3/normal_estimation_test.cpp
+++ b/Point_set_processing_3/test/Point_set_processing_3/normal_estimation_test.cpp
@@ -9,9 +9,6 @@
 //----------------------------------------------------------
 // normal_estimation_test points1.xyz points2.xyz...
 
-// With iterator debugging this testsuite takes to long and the process gets killed
-//#define _HAS_ITERATOR_DEBUGGING 0
-
 // CGAL
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Timer.h>