diff --git a/Nef_2/include/CGAL/Nef_2/PM_overlayer.h b/Nef_2/include/CGAL/Nef_2/PM_overlayer.h
index d32088fa0c5..662efd33c64 100644
--- a/Nef_2/include/CGAL/Nef_2/PM_overlayer.h
+++ b/Nef_2/include/CGAL/Nef_2/PM_overlayer.h
@@ -646,8 +646,9 @@ avoid the simplification for edge pairs referenced by |e|.}*/
   for (f = this->faces_begin(); f != fend; f=fn) {
     fn=f; ++fn;
     Union_find_handle pit = Pitem[f];
-    if (unify_faces.find(pit) != pit) {
       Union_find_handle root = unify_faces.find(pit);
+      if (root != pit) {
+
       for(Isolated_vertex_iterator ivi = isolated_vertices_begin(f); ivi != isolated_vertices_end(f); ++ivi){
         ivi->set_face(*root);
         link_as_isolated_vertex(*root,ivi);
diff --git a/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h b/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
index 6ecc25669e0..1eecd047efd 100644
--- a/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
+++ b/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
@@ -167,7 +167,7 @@ public:
   Point_2 target(const ISegment& is) const
   { return K.target(is->first()); }
 
-  ITERATOR original(xonst ISegment& s) const
+  ITERATOR original(const ISegment& s) const
   { return s->second(); }
 
   int orientation(ST_item sit, const Point_2& p) const