diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
index 1cde09f74c6..817b95f57b8 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
@@ -4,54 +4,64 @@
 #include <iostream>
 #include <fstream>
 
-
 namespace PMP = CGAL::Polygon_mesh_processing;
 
-typedef CGAL::Simple_cartesian<double>                       Kernel;
-typedef Kernel::Point_3                                      Point;
-typedef CGAL::Surface_mesh<Point>                           Mesh;
-
-
-typedef boost::graph_traits<Mesh>::vertex_descriptor vertex_descriptor;
-typedef boost::graph_traits<Mesh>::face_descriptor face_descriptor;
-typedef boost::graph_traits<Mesh>::halfedge_descriptor halfedge_descriptor;
-typedef boost::graph_traits<Mesh>::edge_descriptor edge_descriptor;
+typedef CGAL::Simple_cartesian<double>     Kernel;
+typedef Kernel::Point_3                    Point;
+typedef Kernel::Compare_dihedral_angle_3   Compare_dihedral_angle_3;
+typedef CGAL::Surface_mesh<Point>          Mesh;
 
 
 template <typename G>
 struct Constraint {
-  Constraint() { }
+  typedef typename boost::graph_traits<G>::halfedge_descriptor halfedge_descriptor;
+  typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
 
-  Constraint(G & g) : g(&g) { }
+  Constraint()
+  {}
 
-  bool operator[](const edge_descriptor&) const {
-    return false; // no constraint
+  Constraint(G & g, double bound) 
+    : g(&g), bound(bound)
+  { }
+
+  bool operator[](edge_descriptor e) const {
+    return compare((*g).point(source(e,*g)),
+                   (*g).point(target(e,*g)),
+                   (*g).point(target(next(halfedge(e,*g),*g),*g)),
+                   (*g).point(target(next(opposite(halfedge(e,*g),*g),*g),*g)),
+                   bound) == CGAL::SMALLER;
   }
 
   G* g;
+  Compare_dihedral_angle_3 compare;
+  double bound;
 };
 
  
 int main(int, char* argv[]) 
 {
+  typedef boost::graph_traits<Mesh>::face_descriptor face_descriptor;
+  const double bound = std::cos(0.7* CGAL_PI);
   Mesh sm;
   std::ifstream in(argv[1]);
   in >> sm;
-
+  
   std::vector<face_descriptor> cc;
   face_descriptor fd = *faces(sm).first;
   CGAL::Polygon_mesh_processing::connected_component(fd,
                                                      sm,
                                                      std::back_inserter(cc));
 
-
+  std::cerr << "connected components without edge constraints" << std::endl;
   std::cerr << cc.size() << " faces in the CC of " << fd << std::endl;
 
+
+  std::cerr << "\nconnected components with edge constraints (dihedral angle < 3/4 pi)" << std::endl;
   Mesh::Property_map<face_descriptor,std::size_t> fccmap;
   fccmap = sm.add_property_map<face_descriptor,std::size_t>("f:CC").first; 
   std::size_t num = PMP::connected_components(sm,
                                               fccmap,
-                                              CGAL::parameters::edge_is_constrained_map(Constraint<Mesh>())
+                                              CGAL::parameters::edge_is_constrained_map(Constraint<Mesh>(sm,bound))
                                               );
   
  std::cerr << "The graph has " << num << " connected components (face connectivity)" << std::endl;
@@ -59,7 +69,8 @@ int main(int, char* argv[])
    std::cout  << f << " in connected component " << fccmap[f] << std::endl;
   }
  
- CGAL::Polygon_mesh_processing::keep_largest_connected_components(sm,2);
+ std::cerr << "We keep the two largest components" << std::endl; 
+ PMP::keep_largest_connected_components(sm,2,CGAL::parameters::edge_is_constrained_map(Constraint<Mesh>(sm,bound)));
 
  std::cout << "mesh:\n" << sm << std::endl;
   return 0;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
index d32cb894b91..ca9b330a6bf 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
@@ -620,7 +620,6 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
       // don't care about connectivity
       // As vertices are not kept the faces and vertices will be removed later
       remove_edge(e,pmesh);
-      std::cerr << "after remove_edge"<< std::endl;
     } else if( keep_vertex[v] &&  keep_vertex[w]){
       face_descriptor fh = face(h,pmesh), ofh = face(oh,pmesh);
       if(is_border(h,pmesh) && is_border(oh,pmesh)){