diff --git a/Triangulation_2/include/CGAL/Polyline_constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Polyline_constrained_triangulation_2.h
index 96b9cef5df6..966605d7ae4 100644
--- a/Triangulation_2/include/CGAL/Polyline_constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Polyline_constrained_triangulation_2.h
@@ -190,7 +190,7 @@ public:
   Vertex_handle insert(const Point& p,
 		       Locate_type lt,
 		       Face_handle loc, int li );
-  Constraint_id insert_constraint(const Point& a, const Point& b);
+  Constraint_id insert_constraint(Point a, Point b);
 
   Vertices_in_constraint_iterator
   insert_vertex_in_constraint(Constraint_id cid, Vertices_in_constraint_iterator pos, 
@@ -364,7 +364,7 @@ public:
   }
 
   template < class InputIterator, class OutputIterator>
-  Constraint_id insert_polyline(InputIterator first, InputIterator last, OutputIterator out)
+  Constraint_id insert_constraint(InputIterator first, InputIterator last, OutputIterator out)
   {
     Face_handle hint;
     Face_container<Self> fc(*this);
@@ -415,7 +415,7 @@ public:
   }
 
   template < class InputIterator>
-  Constraint_id insert_polyline(InputIterator first, InputIterator last)
+  Constraint_id insert_constraint(InputIterator first, InputIterator last)
   {
   Face_handle hint;
     std::vector<Vertex_handle> vertices;
@@ -577,6 +577,13 @@ insert_constraint(Vertex_handle va, Vertex_handle vb, OutputIterator out)
   {
     hierarchy.remove_points_from_constraint(cid);
   }
+
+void remove_points_from_constraints()
+  {
+    hierarchy.remove_points_from_constraints();
+  }
+
+
   // CONCATENATE AND SPLIT
 
   // concatenates two constraints
@@ -833,7 +840,7 @@ template <class Tr>
 inline
 typename Polyline_constrained_triangulation_2<Tr>::Constraint_id
 Polyline_constrained_triangulation_2<Tr>::
-insert_constraint(const Point& a, const Point& b)
+insert_constraint(Point a, Point b)
   // insert endpoints first
 {
   Vertex_handle va= insert(a);
diff --git a/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h b/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
index 397d8d9f7f2..235bd8373fa 100644
--- a/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
+++ b/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
@@ -147,8 +147,8 @@ public:
                 Vertices_in_constraint_iterator v,
                 Vertices_in_constraint_iterator w);
 
-  void remove_points_from_constraint(Constraint_id);
-  void remove_points_from_constraints();
+  int remove_points_from_constraint(Constraint_id);
+  int remove_points_from_constraints();
 
   Constraint_id concatenate(Constraint_id first, Constraint_id second);
   Constraint_id concatenate2(Constraint_id first, Constraint_id second);
@@ -534,29 +534,35 @@ void Polyline_constraint_hierarchy_2<T,Data>::simplify(Vertices_in_constraint_it
 
 
 template <class T, class Data>
-void 
+int
 Polyline_constraint_hierarchy_2<T,Data>::remove_points_from_constraint(Constraint_id cid)
 {
+  int n=0;
   Vertices_in_constraint_iterator b = cid->begin(), e = cid->end();
   while(b!=e){
     if(b->removed){
       Vertices_in_constraint_iterator r = b;
       ++b;
       cid->erase(r);
+      ++n;
     }else{
       ++b;
     }
   }
+  return n;
 }
 
 
 template <class T, class Data>
-void 
+int
 Polyline_constraint_hierarchy_2<T,Data>::remove_points_from_constraints()
 {
+  int n = 0;
   for(H_c_iterator it = constraint_set.begin(); it!= constraint_set.end(); ++it){
-    remove_points_from_constraint(*it);
+    n+= remove_points_from_constraint(*it);
   }
+  std::cerr << "Removed " << n << " points" << std::endl;
+  return n;
 }