diff --git a/Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_validation.h b/Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_validation.h
index d5bcafcbdfc..447115ed473 100644
--- a/Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_validation.h
+++ b/Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_polygon_validation.h
@@ -622,7 +622,7 @@ bool are_holes_and_boundary_pairwise_disjoint
                                                         Topology_traits;
   typedef CGAL::Gps_on_surface_base_2<Traits_2, Topology_traits>
                                                         Polygon_set_2;
-  typedef typename Polygon_set_2::Size                  Size;
+  // typedef typename Polygon_set_2::Size                  Size;
   typedef  typename Traits_2::Polygon_2                 Polygon_2;
   typedef typename Traits_2::Polygon_with_holes_2       Polygon_with_holes_2;
   typedef typename Polygon_with_holes_2::Hole_const_iterator
@@ -677,7 +677,7 @@ bool are_holes_and_boundary_pairwise_disjoint
   Polygon_set_2 gps(traits);
   // check for 2D  intersections of holes (holes must be disjoint except for
   // vertices)
-  Size num_of_holes = 0;
+  // Size num_of_holes = 0;
   // functors for creating a pwh needed for inserting pgns into the arrangement
   // quickly
   Construct_polygon_with_holes_2 construct_pwh_functor =
@@ -701,7 +701,7 @@ bool are_holes_and_boundary_pairwise_disjoint
       // traits.Construct_polygon_with_holes_2 (hole);
       // Polygon_with_holes_2 empty_pwh(hole);
       gps.insert(empty_pwh);
-      num_of_holes++;
+    //  num_of_holes++;
     }
   }
   /* not good - doesn't work if intersection at vertices is legal.
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
index 25096d0c26f..35c3104dd7e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/repair_degeneracies.h
@@ -646,6 +646,7 @@ bool remove_almost_degenerate_faces(const FaceRange& face_range,
 {
   using CGAL::parameters::choose_parameter;
   using CGAL::parameters::get_parameter;
+  using parameters::is_default_parameter;
 
   typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor         vertex_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor       halfedge_descriptor;
@@ -702,21 +703,25 @@ bool remove_almost_degenerate_faces(const FaceRange& face_range,
   CGAL_precondition(is_triangle_mesh(tmesh));
 
   // constrain extremities of constrained edges
-  for(face_descriptor f : face_range)
+  if constexpr (!is_default_parameter<NamedParameters, internal_np::edge_is_constrained_t>::value ||
+                !is_default_parameter<NamedParameters, internal_np::vertex_is_constrained_t>::value)
   {
-    if(f == boost::graph_traits<TriangleMesh>::null_face())
-      continue;
-
-    for(halfedge_descriptor h : CGAL::halfedges_around_face(halfedge(f, tmesh), tmesh))
+    for(face_descriptor f : face_range)
     {
-      if(get(ecm, edge(h, tmesh)))
+      if(f == boost::graph_traits<TriangleMesh>::null_face())
+        continue;
+
+      for(halfedge_descriptor h : CGAL::halfedges_around_face(halfedge(f, tmesh), tmesh))
       {
-        put(vcm, source(h, tmesh), true);
-        put(vcm, target(h, tmesh), true);
-      }
-      else if(get(vcm_np, target(h, tmesh)))
-      {
-        put(vcm, target(h, tmesh), true);
+        if(get(ecm, edge(h, tmesh)))
+        {
+          put(vcm, source(h, tmesh), true);
+          put(vcm, target(h, tmesh), true);
+        }
+        else if(get(vcm_np, target(h, tmesh)))
+        {
+          put(vcm, target(h, tmesh), true);
+        }
       }
     }
   }
@@ -813,7 +818,7 @@ bool remove_almost_degenerate_faces(const FaceRange& face_range,
 
       const edge_descriptor e = edge(h, tmesh);
       CGAL_assertion(!get(ecm, edge(h, tmesh)));
-      CGAL_assertion(!get(vcm, source(h, tmesh)) && !get(vcm, target(h, tmesh)));
+      CGAL_assertion(!get(vcm, source(h, tmesh)) || !get(vcm, target(h, tmesh)));
 
 #ifdef CGAL_PMP_DEBUG_REMOVE_DEGENERACIES_EXTRA
       std::cout << "  treat needle: " << e
diff --git a/Triangulation_3/doc/Triangulation_3/CGAL/Regular_triangulation_cell_base_3.h b/Triangulation_3/doc/Triangulation_3/CGAL/Regular_triangulation_cell_base_3.h
index 637595f1e25..d4f3128f817 100644
--- a/Triangulation_3/doc/Triangulation_3/CGAL/Regular_triangulation_cell_base_3.h
+++ b/Triangulation_3/doc/Triangulation_3/CGAL/Regular_triangulation_cell_base_3.h
@@ -75,7 +75,7 @@ circumcenter is not supposed to be computed
 by the constructor `Construct_weighted_circumcenter_3` of the traits
 class, hence the returned point has no weight.
 */
-const Point_3& weighted_circumcenter(const Traits& gt = Traits()) const;
+Point_3 weighted_circumcenter(const Traits& gt = Traits()) const;
 
 /// @}
 
diff --git a/Triangulation_3/include/CGAL/Regular_triangulation_3.h b/Triangulation_3/include/CGAL/Regular_triangulation_3.h
index 97459a258a1..bec183f4e51 100644
--- a/Triangulation_3/include/CGAL/Regular_triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Regular_triangulation_3.h
@@ -665,6 +665,9 @@ public:
   {
     CGAL_precondition(dimension() >= 2);
 
+    if(the_facet_is_in_its_cz)
+      *the_facet_is_in_its_cz = false;
+
     std::vector<Cell_handle> cells;
     cells.reserve(32);
     std::vector<Facet> facets;