diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_polyhedron.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_polyhedron.cpp
index f6303ceb0ec..eb9106546a7 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_polyhedron.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/cc_polyhedron.cpp
@@ -107,10 +107,9 @@ void mesh_no_id(char* argv1)
   boost::vector_property_map<int, typename boost::property_map<Mesh, boost::face_external_index_t>::type> fccmap(fim);
 
   std::size_t num = PMP::connected_components(sm,
-                                              fccmap
-                                              , CGAL::parameters::vertex_index_map(vim)
-                                                                 .face_index_map(fim)
-                                      );
+                                              fccmap,
+                                              PMP::internal::No_constraint<Mesh>(),
+                                              fim);
   
  std::cerr << "The graph has " << num << " connected components (face connectivity)" << std::endl;
  BOOST_FOREACH(face_descriptor f , faces(sm)){
@@ -118,10 +117,10 @@ void mesh_no_id(char* argv1)
   }
  
  PMP::keep_largest_connected_components(sm
-                                        ,2
-                                        , CGAL::parameters::vertex_index_map(vim)
-                                                           .face_index_map(fim)
-);
+   , 2
+   , PMP::internal::No_constraint<Mesh>()
+   , vim
+   , fim);
 
  std::cout << "mesh:\n" << sm << std::endl;
 }
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 817b95f57b8..452d71aa808 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
@@ -61,7 +61,7 @@ int main(int, char* argv[])
   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>(sm,bound))
+                                              Constraint<Mesh>(sm,bound)
                                               );
   
  std::cerr << "The graph has " << num << " connected components (face connectivity)" << std::endl;
@@ -70,7 +70,7 @@ int main(int, char* argv[])
   }
  
  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)));
+ PMP::keep_largest_connected_components(sm,2,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 9e123e14373..9383492925d 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
@@ -384,10 +384,10 @@ template <class PolygonMesh
           = No_edge_constraint<PolygonMesh>
 #endif
           >
-OutputIterator
+FaceOutputIterator
 connected_component(typename boost::graph_traits<PolygonMesh>::face_descriptor seed_face,
                     PolygonMesh& pmesh
-                    ,OutputIterator out
+                    , FaceOutputIterator out
                     , EdgeConstraintMap ecmap
 #ifdef DOXYGEN_RUNNING
                     = EdgeConstraintMap(pmesh)
@@ -536,7 +536,7 @@ connected_components(PolygonMesh& pmesh,
                      EdgeConstraintMap ecmap)
 {
 
-  return CGAL::connected_components(pmesh, fcm, ecmap,get(boost::face_index,pmesh));
+  return CGAL::Polygon_mesh_processing::connected_components(pmesh, fcm, ecmap, get(boost::face_index, pmesh));
 }
 
 
@@ -546,7 +546,7 @@ connected_components(PolygonMesh& pmesh,
                      FaceComponentMap& fcm)
 {
 
-  return CGAL::connected_components(pmesh,
+  return CGAL::Polygon_mesh_processing::connected_components(pmesh,
                                     fcm,
                                     internal::No_constraint<PolygonMesh>(pmesh),
                                     get(boost::face_index,pmesh));
@@ -766,7 +766,8 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
                                               EdgeConstraintMap ecmap,
                                               VertexIndexMap vim)
 {
-  return keep_largest_connected_components(pmesh, nb_components_to_keep, ecmap, vim, get(boost::face_index, pmesh));
+  return keep_largest_connected_components(pmesh, nb_components_to_keep, ecmap, vim,
+                                           get(boost::face_index, pmesh));
 }
 
 template <class PolygonMesh, class EdgeConstraintMap>
@@ -774,7 +775,9 @@ std::size_t keep_largest_connected_components(PolygonMesh& pmesh,
                                               std::size_t nb_components_to_keep,
                                               EdgeConstraintMap ecmap)
 {
-  return keep_largest_connected_components(pmesh, nb_components_to_keep, ecmap, get(boost::vertex_index, pmesh),, get(boost::face_index, pmesh));
+  return keep_largest_connected_components(pmesh, nb_components_to_keep, ecmap,
+                                           get(boost::vertex_index, pmesh),
+                                           get(boost::face_index, pmesh));
 }
 
 template <class PolygonMesh>