diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/remove_degeneracies_example.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/remove_degeneracies_example.cpp
index 59b5de345f2..c90c08cd88f 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/remove_degeneracies_example.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/remove_degeneracies_example.cpp
@@ -24,7 +24,7 @@ int main(int argc, char* argv[])
   std::size_t nb
     = CGAL::Polygon_mesh_processing::remove_degenerate_faces(mesh);
 
-  std::cout << "There were " << nb << " degenerate faces in this mesh" << std::endl;
+  std::cerr << "There were " << nb << " degenerate faces in this mesh" << std::endl;
   mesh.collect_garbage();
   std::cout << mesh << std::endl;
   return 0;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/named_function_params.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/named_function_params.h
index f275a591ac4..7176ffdc4ee 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/named_function_params.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/named_function_params.h
@@ -161,7 +161,7 @@ namespace Polygon_mesh_processing{
 namespace parameters{
 
   pmp_bgl_named_params<bool, all_default_t>
-  all_default()
+  inline all_default()
   {
     typedef pmp_bgl_named_params<bool, all_default_t> Params;
     return Params();
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
index a5f4d83bec3..6b330af8921 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair.h
@@ -281,9 +281,9 @@ std::size_t remove_degenerate_faces(TriangleMesh& tmesh,
   typedef typename GT::vertex_descriptor vertex_descriptor;
 
   typedef typename GetVertexPointMap<TM, NamedParameters>::type VertexPointMap;
-  VertexPointMap vpmap = choose_const_pmap(get_param(np, boost::vertex_point),
-                                           tmesh,
-                                           boost::vertex_point);
+  VertexPointMap vpmap = choose_pmap(get_param(np, boost::vertex_point),
+                                     tmesh,
+                                     boost::vertex_point);
   typedef typename GetGeomTraits<TM, NamedParameters>::type Traits;
   Traits traits = choose_param(get_param(np, geom_traits), Traits());
 
@@ -604,9 +604,9 @@ std::size_t remove_degenerate_faces(TriangleMesh& tmesh,
       typename Traits::Compare_distance_3 compare_distance = traits.compare_distance_3_object();
 
       halfedge_descriptor edge_to_flip;
-      if (!compare_distance(p1,p2, p1,p3)) // p1p2 > p1p3
+      if (compare_distance(p1,p2, p1,p3) != CGAL::SMALLER) // p1p2 > p1p3
       {
-        if (!compare_distance(p1,p2, p2,p3)) // p1p2 > p2p3
+        if (compare_distance(p1,p2, p2,p3) != CGAL::SMALLER) // p1p2 > p2p3
           // flip p1p2
           edge_to_flip = next( halfedge(fd, tmesh), tmesh );
         else
@@ -614,7 +614,7 @@ std::size_t remove_degenerate_faces(TriangleMesh& tmesh,
           edge_to_flip = prev( halfedge(fd, tmesh), tmesh );
       }
       else
-        if (!compare_distance(p1,p3, p2,p3)) // p1p3>p2p3
+        if (compare_distance(p1,p3, p2,p3) != CGAL::SMALLER) // p1p3>p2p3
           //flip p3p1
           edge_to_flip = halfedge(fd, tmesh);
         else