diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
index b78f7465e96..7b092da9df8 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/Concepts/ErrorMetricProxy.h
@@ -26,7 +26,7 @@ public:
   /// @{
 
   /// Computes and returns fitting error from face f to proxy.
-  FT compute_error(const TriangleMesh &tm, const face_descriptor &f, const Proxy &proxy) const;
+  FT compute_error(const TriangleMesh &tm, const face_descriptor f, const Proxy &proxy) const;
 
   /// Computes and returns fitted proxy from a range of faces.
   /// @tparam FaceRange a range of
diff --git a/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
index 71c1a6ac8e4..64dd6ddabbf 100644
--- a/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/L21_metric_plane_proxy.h
@@ -85,7 +85,7 @@ public:
    * @param px proxy
    * @return computed error
    */
-  FT compute_error(const TriangleMesh &tm, const face_descriptor &f, const Proxy &px) const {
+  FT compute_error(const TriangleMesh &tm, const face_descriptor f, const Proxy &px) const {
     (void)(tm);
     Vector_3 v = m_sum_functor(get(m_fnmap, f), m_scale_functor(px, FT(-1.0)));
     return get(m_famap, f) * m_scalar_product_functor(v, v);
@@ -105,7 +105,7 @@ public:
 
     // fitting normal
     Vector_3 norm = CGAL::NULL_VECTOR;
-    BOOST_FOREACH(const face_descriptor &f, faces) {
+    BOOST_FOREACH(const face_descriptor f, faces) {
       norm = m_sum_functor(norm,
         m_scale_functor(get(m_fnmap, f), get(m_famap, f)));
     }
diff --git a/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
index 1174a8f521f..53d4643234f 100644
--- a/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/L2_metric_plane_proxy.h
@@ -77,7 +77,7 @@ public:
    * @param px proxy
    * @return computed error
    */
-  FT compute_error(const TriangleMesh &tm, const face_descriptor &f, const Proxy &px) const {
+  FT compute_error(const TriangleMesh &tm, const face_descriptor f, const Proxy &px) const {
     (void)(tm);
     halfedge_descriptor he = halfedge(f, *m_tm);
     const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
@@ -110,7 +110,7 @@ public:
     CGAL_assertion(!faces.empty());
 
     std::list<Triangle_3> tris;
-    BOOST_FOREACH(const face_descriptor &f, faces) {
+    BOOST_FOREACH(const face_descriptor f, faces) {
       const halfedge_descriptor he = halfedge(f, *m_tm);
       const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
       const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
diff --git a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
index 3c786bb95d2..baa59633dfa 100644
--- a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
@@ -134,7 +134,7 @@ public:
 #endif
   // The proxy wrapper for approximation.
   struct Proxy_wrapper {
-    Proxy_wrapper(const Proxy &p, const std::size_t &i, const face_descriptor &s, const FT &e)
+    Proxy_wrapper(const Proxy &p, const std::size_t &i, const face_descriptor s, const FT &e)
       : px(p), idx(i), seed(s), err(e) {}
 
     Proxy px; // parameterized proxy
@@ -158,7 +158,7 @@ private:
 
   // The facet candidate to be queued.
   struct Facet_to_integrate {
-    Facet_to_integrate(const face_descriptor &f_, const std::size_t &px_, const FT &err_)
+    Facet_to_integrate(const face_descriptor f_, const std::size_t &px_, const FT &err_)
       : f(f_), px(px_), err(err_) {}
 
     bool operator<(const Facet_to_integrate &rhs) const {