diff --git a/Nef_3/include/CGAL/Nef_3/SNC_const_decorator.h b/Nef_3/include/CGAL/Nef_3/SNC_const_decorator.h
index 910ba280e2f..c2c622a181e 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_const_decorator.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_const_decorator.h
@@ -539,12 +539,6 @@ visit_shell_objects(typename Traits::SFace_handle f, Visitor& V) const
             if ((f->incident_volume() == tf->incident_volume()) && Done[tf]) {
                 continue; // for example when we have to do with the unbounded volume and a surface with boundaries
             }
-            Volume_const_iterator unbounded = volumes_begin();
-            Volume_const_iterator fit = f->incident_volume();
-            Volume_const_iterator tfit = tf->incident_volume();
-            if ((fit == unbounded) && (tfit != unbounded)) {
-                continue; // because we will later report it from the bounded side
-            }
             FacetCandidates.push_back(f); Done[f] = true;
           }
         } else if (fc.is_svertex() ) {
diff --git a/Nef_3/include/CGAL/boost/graph/convert_nef_polyhedron_to_polygon_mesh.h b/Nef_3/include/CGAL/boost/graph/convert_nef_polyhedron_to_polygon_mesh.h
index f2a880c8872..bb11c0daace 100644
--- a/Nef_3/include/CGAL/boost/graph/convert_nef_polyhedron_to_polygon_mesh.h
+++ b/Nef_3/include/CGAL/boost/graph/convert_nef_polyhedron_to_polygon_mesh.h
@@ -359,14 +359,28 @@ void convert_nef_polyhedron_to_polygon_soup(const Nef_polyhedron& nef,
   CGAL_assertion ( vol_it != vol_end );
 
   Converter to_output;
+  bool handling_unbounded_volume = true;
+
+  auto shell_is_closed = [](typename Nef_polyhedron::SFace_const_handle sfh)
+  {
+    typename Nef_polyhedron::Halffacet_handle f = sfh;
+    return f->incident_volume()!=f->twin()->incident_volume();
+  };
+
   for (;vol_it!=vol_end;++vol_it)
+  {
     for(auto sit = vol_it->shells_begin(); sit != vol_it->shells_end(); ++sit)
+    {
+      if ( (handling_unbounded_volume || sit!=vol_it->shells_begin()) && shell_is_closed(sit)) continue;
       nef_to_pm::collect_polygon_mesh_info(points,
                                            polygons,
                                            nef,
                                            sit,
                                            to_output,
                                            triangulate_all_faces);
+    }
+    handling_unbounded_volume = false;
+  }
 }
 
 template <class Nef_polyhedron, class Polygon_mesh>