diff --git a/Mesh_3/include/CGAL/make_mesh_3.h b/Mesh_3/include/CGAL/make_mesh_3.h
index 64105159344..7160b9944d4 100644
--- a/Mesh_3/include/CGAL/make_mesh_3.h
+++ b/Mesh_3/include/CGAL/make_mesh_3.h
@@ -417,7 +417,7 @@ struct C3t3_initializer < C3T3, MD, MC, true, CGAL::Tag_false >
  * \sa `odt_optimize_mesh_3()`
  */
 template<typename C3T3, typename MeshDomain, typename MeshCriteria, typename CGAL_NP_TEMPLATE_PARAMETERS>
-C3T3 make_mesh_3(MeshDomain& domain, MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
+C3T3 make_mesh_3(const MeshDomain& domain, const MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
 {
     using parameters::choose_parameter;
     using parameters::get_parameter;
@@ -443,7 +443,7 @@ template<typename C3T3, typename MeshDomain, typename MeshCriteria,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-C3T3 make_mesh_3(MeshDomain& domain, MeshCriteria& criteria,
+C3T3 make_mesh_3(const MeshDomain& domain, const MeshCriteria& criteria,
                  const CGAL_NP_CLASS_1&  np1,
                  const CGAL_NP_CLASS_2&  np2,
                  const NP& ... nps)
diff --git a/Mesh_3/include/CGAL/refine_mesh_3.h b/Mesh_3/include/CGAL/refine_mesh_3.h
index 94a44676b0c..3f11e81ce8a 100644
--- a/Mesh_3/include/CGAL/refine_mesh_3.h
+++ b/Mesh_3/include/CGAL/refine_mesh_3.h
@@ -261,7 +261,7 @@ private:
  * \sa `CGAL::parameters::no_odt()`
  */
 template<typename C3T3, typename MeshDomain, typename MeshCriteria, typename CGAL_NP_TEMPLATE_PARAMETERS>
-void refine_mesh_3(C3T3& c3t3, MeshDomain& domain, MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
+void refine_mesh_3(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria, const CGAL_NP_CLASS& np = parameters::default_values())
 {
     using parameters::choose_parameter;
     using parameters::get_parameter;
@@ -291,7 +291,7 @@ template<typename C3T3, typename MeshDomain, typename MeshCriteria,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
          typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
          typename ... NP>
-void refine_mesh_3(C3T3& c3t3, MeshDomain& domain, MeshCriteria& criteria,
+void refine_mesh_3(C3T3& c3t3, const MeshDomain& domain, const MeshCriteria& criteria,
                    const CGAL_NP_CLASS_1&  np1,
                    const CGAL_NP_CLASS_2&  np2,
                    const NP& ... nps)