diff --git a/Mesh_3/include/CGAL/make_mesh_3.h b/Mesh_3/include/CGAL/make_mesh_3.h
index 6c04b14b67b..8c1581368f4 100644
--- a/Mesh_3/include/CGAL/make_mesh_3.h
+++ b/Mesh_3/include/CGAL/make_mesh_3.h
@@ -41,7 +41,7 @@ namespace internal {
 template < typename C3T3, typename MeshDomain, typename MeshCriteria, typename InitialPointsGenerator = Null_functor >
 void
 init_c3t3(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria&,
-          const int nb_initial_points, InitialPointsGenerator& generator = Null_functor())
+          const int nb_initial_points, InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
 {
   typedef typename MeshDomain::Point_3 Point_3;
   typedef typename MeshDomain::Index Index;
@@ -184,7 +184,7 @@ struct C3t3_initializer < C3T3, MD, MC, false, HasFeatures, InitialPointsGenerat
                   const MC& criteria,
                   bool with_features,
                   Mesh_3_options mesh_options = Mesh_3_options(),
-                  InitialPointsGenerator& generator = Null_functor())
+                  InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
   {
     if ( with_features )
     {
@@ -208,7 +208,7 @@ struct C3t3_initializer < C3T3, MD, MC, true, HasFeatures, InitialPointsGenerato
                   const MC& criteria,
                   bool with_features,
                   Mesh_3_options mesh_options = Mesh_3_options(),
-                  InitialPointsGenerator& generator = Null_functor())
+                  InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
   {
     C3t3_initializer < C3T3, MD, MC, true, typename MD::Has_features, InitialPointsGenerator >()
       (c3t3,domain,criteria,with_features,mesh_options,generator);
@@ -230,7 +230,7 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_true, InitialPointsGener
                   const MC& criteria,
                   bool with_features,
                   Mesh_3_options mesh_options = Mesh_3_options(),
-                  InitialPointsGenerator& generator = Null_functor())
+                  InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
   {
     if ( with_features ) {
       this->initialize_features(c3t3, domain, criteria,mesh_options);
@@ -276,7 +276,7 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_false, InitialPointsGene
                   const MC& criteria,
                   bool with_features,
                   Mesh_3_options mesh_options = Mesh_3_options(),
-                  InitialPointsGenerator& generator = Null_functor())
+                  InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
   {
     if ( with_features )
     {
@@ -524,7 +524,7 @@ void make_mesh_3_impl(C3T3& c3t3,
                         mesh_options = parameters::internal::Mesh_3_options(),
                       const parameters::internal::Manifold_options&
                         manifold_options = parameters::internal::Manifold_options(),
-                      InitialPointsGenerator& generator = Null_functor())
+                      InitialPointsGenerator& generator = Null_functor_internal::default_null_functor)
 {
 #ifdef CGAL_MESH_3_INITIAL_POINTS_NO_RANDOM_SHOOTING
   CGAL::get_default_random() = CGAL::Random(0);
diff --git a/STL_Extension/include/CGAL/STL_Extension/internal/mesh_option_classes.h b/STL_Extension/include/CGAL/STL_Extension/internal/mesh_option_classes.h
index 195a7a271cb..97defe20378 100644
--- a/STL_Extension/include/CGAL/STL_Extension/internal/mesh_option_classes.h
+++ b/STL_Extension/include/CGAL/STL_Extension/internal/mesh_option_classes.h
@@ -188,8 +188,8 @@ struct Initial_points_generator_wrapper
   }
 
 private:
-  std::function<OutputIterator(OutputIterator,MeshDomain,C3t3)> initial_points_generator_default_;
-  std::function<OutputIterator(OutputIterator,MeshDomain,C3t3,int)> initial_points_generator_;
+  const std::function<OutputIterator(OutputIterator,MeshDomain,C3t3)> initial_points_generator_default_;
+  const std::function<OutputIterator(OutputIterator,MeshDomain,C3t3,int)> initial_points_generator_;
 };
 template <typename OutputIterator, typename MeshDomain, typename C3t3>
 struct Initial_points_generator_default
diff --git a/STL_Extension/include/CGAL/tags.h b/STL_Extension/include/CGAL/tags.h
index 6aa1988e1cc..1fcff383e3e 100644
--- a/STL_Extension/include/CGAL/tags.h
+++ b/STL_Extension/include/CGAL/tags.h
@@ -53,6 +53,9 @@ struct Null_functor {
   typedef Null_tag result_type;
   typedef Null_tag second_argument_type;
 };
+namespace Null_functor_internal {
+  static Null_functor default_null_functor;
+}
 
 // For concurrency
 struct Sequential_tag {};