diff --git a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
index 36d57935a4d..eef7058ba6d 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
@@ -1197,6 +1197,7 @@ insert_balls(const Vertex_handle& vp,
                            dim,
                            index,
                            out);
+      if(forced_stop()) return out;
       const Vertex_handle new_vertex = pair.first;
       out = pair.second;
       const FT sn = get_radius(new_vertex);
@@ -1835,6 +1836,7 @@ walk_along_edge(const Vertex_handle& start, const Vertex_handle& next,
   // and current intersects enough
   while ( ! is_sampling_dense_enough(previous, current, curve_index, orientation) )
   {
+    if(forced_stop()) return out;
     *out++ = current;
 
     // Don't go through corners
@@ -1943,6 +1945,7 @@ repopulate(InputIterator begin, InputIterator last,
 #endif // CGAL_MESH_3_PROTECTION_DEBUG
     *out++ = *current;
     c3t3_.triangulation().remove(*current);
+    if(forced_stop()) return out;
   }
 
   // Repopulate edge
diff --git a/Mesh_3/include/CGAL/make_mesh_3.h b/Mesh_3/include/CGAL/make_mesh_3.h
index 6b6e9cb3353..8c40a8c05cd 100644
--- a/Mesh_3/include/CGAL/make_mesh_3.h
+++ b/Mesh_3/include/CGAL/make_mesh_3.h
@@ -197,7 +197,13 @@ template < typename C3T3, typename MeshDomain, typename MeshCriteria>
 void init_c3t3_with_features(C3T3& c3t3,
                              const MeshDomain& domain,
                              const MeshCriteria& criteria,
-                             bool nonlinear = false)
+                             bool nonlinear = false,
+                             std::size_t maximal_number_of_vertices = 0,
+                             Mesh_error_code* pointer_to_error_code = 0
+#ifndef CGAL_NO_ATOMIC
+                             , CGAL::cpp11::atomic<bool>* pointer_to_stop = 0
+#endif
+                             )
 {
   typedef typename MeshCriteria::Edge_criteria Edge_criteria;
   typedef Edge_criteria_sizing_field_wrapper<Edge_criteria> Sizing_field;
@@ -206,7 +212,12 @@ void init_c3t3_with_features(C3T3& c3t3,
     protect_edges(c3t3,
                   domain,
                   Sizing_field(criteria.edge_criteria_object()),
-                  typename Edge_criteria::FT()
+                  typename Edge_criteria::FT(),
+                  maximal_number_of_vertices,
+                  pointer_to_error_code
+#ifndef CGAL_NO_ATOMIC
+                  , pointer_to_stop
+#endif
                   );
   protect_edges.set_nonlinear_growth_of_balls(nonlinear);
 
@@ -234,7 +245,13 @@ struct C3t3_initializer_base
   {
     return Mesh_3::internal::init_c3t3_with_features
       (c3t3, domain, criteria,
-       mesh_options.nonlinear_growth_of_balls);
+       mesh_options.nonlinear_growth_of_balls,
+       mesh_options.maximal_number_of_vertices,
+       mesh_options.pointer_to_error_code
+#ifndef CGAL_NO_ATOMIC
+       , mesh_options.pointer_to_stop_atomic_boolean
+#endif
+       );
   }
 };
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
index 0408113e335..0188d438c2b 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
+++ b/Polyhedron/demo/Polyhedron/Plugins/Mesh_3/Mesh_function.h
@@ -136,8 +136,8 @@ private:
 private:
   boost::any object_to_destroy;
   C3t3& c3t3_;
-  Domain* domain_;
-  Mesh_parameters p_;
+  Domain* const domain_;
+  Mesh_parameters const p_;
   std::atomic<bool> stop_;
   Mesher* mesher_;
 #ifdef CGAL_MESH_3_MESHER_STATUS_ACTIVATED
@@ -237,6 +237,7 @@ Mesh_function<D_,Tag>::
 initialize(const Mesh_criteria& criteria, Mesh_fnt::Domain_tag)
 // for the other domain types
 {
+  namespace p = CGAL::parameters;
   // Initialization of the mesh, either with the protection of sharp
   // features, or with the initial points (or both).
   // If `detect_connected_components==true`, the initialization is
@@ -250,7 +251,9 @@ initialize(const Mesh_criteria& criteria, Mesh_fnt::Domain_tag)
      *domain_,
      criteria,
      p_.protect_features,
-     p_.use_sizing_field_with_aabb_tree);
+     p::mesh_3_options(p::pointer_to_stop_atomic_boolean = &stop_,
+                       p::nonlinear_growth_of_balls =
+                       p_.use_sizing_field_with_aabb_tree));
 }
 
 template < typename D_, typename Tag >