diff --git a/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_policies_2.h b/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_policies_2.h
index 0069b9ce348..ea910ea4424 100644
--- a/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_policies_2.h
+++ b/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_policies_2.h
@@ -44,7 +44,7 @@ struct Regular_triangulation_degeneracy_removal_policy_2
    CGAL_VORONOI_DIAGRAM_2_INS::Regular_triangulation_edge_tester_2<RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Identity_face_rejector<RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Default_site_inserter
-   <typename RT2::Geom_traits::Point_2,RT2>,
+   <typename RT2::Geom_traits::Weighted_point_2,RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Default_site_remover<RT2> >
 {
   typedef typename RT2::Geom_traits::Weighted_point_2  Site_2;
@@ -62,7 +62,7 @@ struct Regular_triangulation_caching_degeneracy_removal_policy_2
    CGAL_VORONOI_DIAGRAM_2_INS::Regular_triangulation_edge_tester_2<RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Identity_face_rejector<RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Default_site_inserter
-   <typename RT2::Geom_traits::Point_2,RT2>,
+   <typename RT2::Geom_traits::Weighted_point_2,RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Default_site_remover<RT2> >
 {
   typedef typename RT2::Geom_traits::Weighted_point_2  Site_2;
diff --git a/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_traits_2.h b/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_traits_2.h
index c8a9656d157..58e8dcde090 100644
--- a/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_traits_2.h
+++ b/Voronoi_diagram_2/include/CGAL/Regular_triangulation_adaptation_traits_2.h
@@ -38,7 +38,7 @@ struct Regular_triangulation_adaptation_traits_2
   : public CGAL_VORONOI_DIAGRAM_2_INS::Adaptation_traits_base_2
   <RT2,
    CGAL_VORONOI_DIAGRAM_2_INS::Point_accessor
-   <typename RT2::Geom_traits::Point_2,RT2,Tag_false>,
+   <typename RT2::Geom_traits::Weighted_point_2,RT2,Tag_false>,
    CGAL_VORONOI_DIAGRAM_2_INS::Regular_triangulation_Voronoi_point_2<RT2>,
    CGAL_VORONOI_DIAGRAM_2_INS::Regular_triangulation_nearest_site_2<RT2> >
 {