diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
index 0e73e595a7a..26552261f4c 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_metric_example.cpp
@@ -30,7 +30,7 @@ struct CompactMetric {
   CompactMetric(const FacetCenterMap &_center_pmap)
     : center_pmap(_center_pmap) {}
 
-  FT operator()(const Facet_const_handle &f, const PointProxy &px) {
+  FT operator()(const Facet_const_handle &f, const PointProxy &px) const {
     return FT(std::sqrt(CGAL::to_double(
       CGAL::squared_distance(center_pmap[f], px.center))));
   }
@@ -45,7 +45,7 @@ struct PointProxyFitting {
     area_pmap(_area_pmap) {}
 
   template<typename FacetIterator>
-  PointProxy operator()(const FacetIterator beg, const FacetIterator end) {
+  PointProxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
     // fitting center
diff --git a/Surface_mesh_approximation/include/CGAL/internal/Surface_mesh_approximation/VSA.h b/Surface_mesh_approximation/include/CGAL/internal/Surface_mesh_approximation/VSA.h
index 73bcf307415..358a326350e 100644
--- a/Surface_mesh_approximation/include/CGAL/internal/Surface_mesh_approximation/VSA.h
+++ b/Surface_mesh_approximation/include/CGAL/internal/Surface_mesh_approximation/VSA.h
@@ -65,10 +65,10 @@ private:
   std::vector<Proxy> proxies;
 
   // The error metric.
-  ErrorMetric fit_error;
+  const ErrorMetric &fit_error;
 
   // The proxy fitting functor.
-  ProxyFitting proxy_fitting;
+  const ProxyFitting &proxy_fitting;
 
   //member functions
 public:
diff --git a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
index 014616619b5..374c2ca1399 100644
--- a/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
+++ b/Surface_mesh_approximation/include/CGAL/vsa_mesh_approximation_traits.h
@@ -46,7 +46,7 @@ struct L21Metric
   typedef typename GeomTraits::Compute_scalar_product_3 Compute_scalar_product_3;
   typedef typename FacetAreaMap::key_type face_descriptor;
 
-  FT operator()(const face_descriptor &f, const PlaneProxy &px) {
+  FT operator()(const face_descriptor &f, const PlaneProxy &px) const {
     Vector_3 v = sum_functor(normal_pmap[f], scale_functor(px.normal, FT(-1)));
     return area_pmap[f] * scalar_product_functor(v, v);
   }
@@ -78,7 +78,7 @@ struct L21ProxyFitting
 
   // Fit and construct a proxy
   template<typename FacetIterator>
-  PlaneProxy operator()(const FacetIterator beg, const FacetIterator end) {
+  PlaneProxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
     // fitting normal
@@ -222,7 +222,7 @@ struct L2Metric
   typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
   typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
 
-  FT operator()(const face_descriptor &f, const PlaneProxy &px) {
+  FT operator()(const face_descriptor &f, const PlaneProxy &px) const {
     halfedge_descriptor he = halfedge(f, mesh);
     const Point_3 &p0 = point_pmap[source(he, mesh)];
     const Point_3 &p1 = point_pmap[target(he, mesh)];
@@ -257,7 +257,7 @@ struct L2ProxyFitting
     : mesh(_mesh), point_pmap(_point_pmap) {}
 
   template<typename FacetIterator>
-  PlaneProxy operator()(const FacetIterator beg, const FacetIterator end) {
+  PlaneProxy operator()(const FacetIterator beg, const FacetIterator end) const {
     CGAL_assertion(beg != end);
 
     std::list<Triangle_3> tris;