diff --git a/Subdivision_method_3/include/CGAL/Subdivision_method_3.h b/Subdivision_method_3/include/CGAL/Subdivision_method_3.h
index f7b46f9518f..1b87ddfb72a 100644
--- a/Subdivision_method_3/include/CGAL/Subdivision_method_3.h
+++ b/Subdivision_method_3/include/CGAL/Subdivision_method_3.h
@@ -42,7 +42,9 @@ namespace CGAL {
 namespace Subdivision_method_3 {
 
   namespace parameters = Polygon_mesh_processing::parameters;
-  //
+
+  // ---------------------------------------------------------------------------
+
   template <class PolygonMesh, class Mask>
   void PQQ(PolygonMesh& pmesh, Mask mask, int step = 1) {
     // todo:  static assert that PolygonMesh == Mask::PolygonMesh
@@ -64,70 +66,6 @@ namespace Subdivision_method_3 {
       Private::PQQ_1step(pmesh, vpm, mask);
   }
 
-  //
-  template <class PolygonMesh,  class Mask>
-  void PTQ(PolygonMesh& pmesh, Mask mask, int step = 1) {
-    for (int i = 0; i < step; i++)
-      Private::PTQ_1step(pmesh, get(vertex_point,pmesh), mask);
-  }
-
-  template <class PolygonMesh, class Mask, class NamedParameters>
-  void PTQ(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
-    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
-    using boost::choose_param;
-    using boost::get_param;
-    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
-    Vpm vpm = choose_param(get_param(np, vertex_point),
-                           get_property_map(CGAL::vertex_point, pmesh));
-
-    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
-    for (unsigned int i = 0; i < step; i++)
-      Private::PTQ_1step(pmesh, vpm, mask);
-  }
-
-  //
-  template <class PolygonMesh, class Mask>
-  void DQQ(PolygonMesh& pmesh, Mask mask, int step = 1) {
-    for (int i = 0; i < step; ++i)
-      Private::DQQ_1step(pmesh, get(vertex_point, pmesh), mask);
-  }
-
-  template <class PolygonMesh, class Mask, class NamedParameters>
-  void DQQ(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
-    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
-    using boost::choose_param;
-    using boost::get_param;
-    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
-    Vpm vpm = choose_param(get_param(np, vertex_point),
-                           get_property_map(CGAL::vertex_point, pmesh));
-
-    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
-    for (unsigned int i = 0; i < step; i++)
-      Private::DQQ_1step(pmesh, vpm, mask);
-  }
-
-  //
-  template <class PolygonMesh, class Mask>
-  void Sqrt3(PolygonMesh& pmesh, Mask mask, int step = 1) {
-    for (int i = 0; i < step; i++)
-      Private::Sqrt3_1step(pmesh, get(vertex_point,pmesh), mask);
-  }
-
-  template <class PolygonMesh, class Mask, class NamedParameters>
-  void Sqrt3(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
-    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
-    using boost::choose_param;
-    using boost::get_param;
-    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
-    Vpm vpm = choose_param(get_param(np, vertex_point),
-                           get_property_map(CGAL::vertex_point, pmesh));
-
-    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
-    for (unsigned int i = 0; i < step; i++)
-      Private::Sqrt3_1step(pmesh, vpm, mask);
-  }
-
-  //
   template <class PolygonMesh>
   void CatmullClark_subdivision(PolygonMesh& pmesh, int step = 1) {
     PQQ(pmesh, CatmullClark_mask_3<PolygonMesh>(pmesh,get(vertex_point,pmesh)), step);
@@ -148,7 +86,28 @@ namespace Subdivision_method_3 {
       Private::PQQ_1step(pmesh, vpm, mask);
   }
 
-  //
+  // ---------------------------------------------------------------------------
+
+  template <class PolygonMesh,  class Mask>
+  void PTQ(PolygonMesh& pmesh, Mask mask, int step = 1) {
+    for (int i = 0; i < step; i++)
+      Private::PTQ_1step(pmesh, get(vertex_point,pmesh), mask);
+  }
+
+  template <class PolygonMesh, class Mask, class NamedParameters>
+  void PTQ(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
+    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
+    using boost::choose_param;
+    using boost::get_param;
+    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
+    Vpm vpm = choose_param(get_param(np, vertex_point),
+                           get_property_map(CGAL::vertex_point, pmesh));
+
+    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
+    for (unsigned int i = 0; i < step; i++)
+      Private::PTQ_1step(pmesh, vpm, mask);
+  }
+
   template <class PolygonMesh>
   void Loop_subdivision(PolygonMesh& pmesh, int step = 1) {
     PTQ(pmesh, Loop_mask_3<PolygonMesh>(pmesh,get(vertex_point,pmesh)) , step);
@@ -169,7 +128,29 @@ namespace Subdivision_method_3 {
       Private::PTQ_1step(pmesh, vpm, mask);
   }
 
-  //
+  // ---------------------------------------------------------------------------
+
+  template <class PolygonMesh, class Mask>
+  void DQQ(PolygonMesh& pmesh, Mask mask, int step = 1) {
+    for (int i = 0; i < step; ++i) {
+      Private::DQQ_1step(pmesh, get(vertex_point, pmesh), mask);
+    }
+  }
+
+  template <class PolygonMesh, class Mask, class NamedParameters>
+  void DQQ(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
+    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
+    using boost::choose_param;
+    using boost::get_param;
+    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
+    Vpm vpm = choose_param(get_param(np, vertex_point),
+                           get_property_map(CGAL::vertex_point, pmesh));
+
+    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
+    for (unsigned int i = 0; i < step; i++)
+      Private::DQQ_1step(pmesh, vpm, mask);
+  }
+
   template <class PolygonMesh>
   void DooSabin_subdivision(PolygonMesh& pmesh, int step = 1) {
     DQQ(pmesh, DooSabin_mask_3<PolygonMesh>(pmesh, get(vertex_point,pmesh)), step);
@@ -190,7 +171,28 @@ namespace Subdivision_method_3 {
       Private::DQQ_1step(pmesh, vpm, mask);
   }
 
-  //
+  // ---------------------------------------------------------------------------
+
+  template <class PolygonMesh, class Mask>
+  void Sqrt3(PolygonMesh& pmesh, Mask mask, int step = 1) {
+    for (int i = 0; i < step; i++)
+      Private::Sqrt3_1step(pmesh, get(vertex_point,pmesh), mask, (i%2==1));
+  }
+
+  template <class PolygonMesh, class Mask, class NamedParameters>
+  void Sqrt3(PolygonMesh& pmesh, Mask mask, const NamedParameters& np) {
+    // todo:  static assert that PolygonMesh == Mask::PolygonMesh
+    using boost::choose_param;
+    using boost::get_param;
+    typedef typename GetVertexPointMap<PolygonMesh, NamedParameters>::type Vpm;
+    Vpm vpm = choose_param(get_param(np, vertex_point),
+                           get_property_map(CGAL::vertex_point, pmesh));
+
+    unsigned int step = choose_param(get_param(np, number_of_iterations), 1);
+    for (unsigned int i = 0; i < step; i++)
+      Private::Sqrt3_1step(pmesh, vpm, mask, (i%2==1));
+  }
+
   template <class PolygonMesh>
   void Sqrt3_subdivision(PolygonMesh& pmesh, int step = 1) {
     Sqrt3(pmesh, Sqrt3_mask_3<PolygonMesh>(pmesh,get(vertex_point,pmesh)), step);
@@ -208,9 +210,11 @@ namespace Subdivision_method_3 {
     Sqrt3_mask_3<PolygonMesh,Vpm> mask(pmesh,vpm);
 
     for(unsigned int i = 0; i < step; i++)
-      Private::Sqrt3_1step(pmesh, vpm, mask);
+      Private::Sqrt3_1step(pmesh, vpm, mask, (i%2==1));
   }
 
+  // ---------------------------------------------------------------------------
+
 }
 
 } //namespace CGAL