diff --git a/Surface_mesh_approximation/doc/Surface_mesh_approximation/NamedParameters.txt b/Surface_mesh_approximation/doc/Surface_mesh_approximation/NamedParameters.txt
index 259a5125667..bb5dbbe22ca 100644
--- a/Surface_mesh_approximation/doc/Surface_mesh_approximation/NamedParameters.txt
+++ b/Surface_mesh_approximation/doc/Surface_mesh_approximation/NamedParameters.txt
@@ -146,7 +146,7 @@ set the plane approximated with the PCA algorithm in the meshing step.\n
 
 \cgalNPBegin{face_proxy_map} \anchor VSA_face_proxy_map
 the property map outputs the proxy index of each face of the input polygon mesh.\n
-\b Type: a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%face_descriptor` as key type and the value type `std::size_t`\n
+\b Type: a class model of `WritablePropertyMap` with `boost::graph_traits<TriangleMesh>::%face_descriptor` as key type and the value type `std::size_t`\n
 \b Default : if this parameter is omitted, no output operation is performed
 \cgalNPEnd
 
diff --git a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L21_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L21_metric_plane_proxy.h
index 035854d4378..71a446118bf 100644
--- a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L21_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L21_metric_plane_proxy.h
@@ -41,7 +41,7 @@ namespace Surface_mesh_approximation {
 /// \cgalModels `ErrorMetricProxy`
 ///
 /// @tparam TriangleMesh a triangle `FaceGraph`
-/// @tparam VertexPointMap a property map with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
+/// @tparam VertexPointMap a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
 ///    as key type, GeomTraits::Point_3 as value type
 /// @tparam GeomTraits a model of Kernel
 template <typename TriangleMesh,
diff --git a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L2_metric_plane_proxy.h b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L2_metric_plane_proxy.h
index cd1b317e860..7589e4e2398 100644
--- a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L2_metric_plane_proxy.h
+++ b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/L2_metric_plane_proxy.h
@@ -44,7 +44,7 @@ namespace Surface_mesh_approximation {
 /// \cgalModels `ErrorMetricProxy`
 ///
 /// @tparam TriangleMesh a triangle `FaceGraph`
-/// @tparam VertexPointMap a property map with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
+/// @tparam VertexPointMap a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
 ///    as key type, GeomTraits::Point_3 as value type
 /// @tparam GeomTraits a model of Kernel
 template <typename TriangleMesh,
diff --git a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
index 27f00b989ec..62fd0fbd27a 100644
--- a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
+++ b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
@@ -111,7 +111,7 @@ unspecified_type all_default();
  *  \cgalParamEnd
  * \cgalNamedParamsEnd
  * \cgalNamedParamsBegin{Output Named Parameters}
- *  \cgalParamBegin{face_proxy_map} a ReadWritePropertyMap with
+ *  \cgalParamBegin{face_proxy_map} a `WritablePropertyMap` with
  * `boost::graph_traits<TriangleMesh>::%face_descriptor` as key and `std::size_t` as value type.
  * A proxy is a set of connected faces which are placed under the same proxy patch (see \cgalFigureRef{iterations}).
  * The proxy-ids are contiguous in range [0, number_of_proxies - 1].
diff --git a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
index a9b174766a2..ebcf0b15d6d 100644
--- a/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
+++ b/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h
@@ -872,7 +872,7 @@ public:
    * @param np optional sequence of \ref vsa_namedparameters among the ones listed below
 
    * \cgalNamedParamsBegin{Output Named Parameters}
-   *  \cgalParamBegin{face_proxy_map} a ReadWritePropertyMap with
+   *  \cgalParamBegin{face_proxy_map} a `WritePropertyMap` with
    * `boost::graph_traits<TriangleMesh>::%face_descriptor` as key and `std::size_t` as value type.
    * A proxy is a set of connected faces which are placed under the same proxy patch (see \cgalFigureRef{iterations}).
    * The proxy-ids are contiguous in range `[0, number_of_proxies() - 1]`.
@@ -917,7 +917,7 @@ public:
   template <typename FaceProxyMap>
   void proxy_map(FaceProxyMap face_proxy_map) const {
     BOOST_FOREACH(face_descriptor f, faces(*m_ptm))
-      face_proxy_map[f] = get(m_fproxy_map, f);
+      put(face_proxy_map, f, get(m_fproxy_map, f));
   }
 
   void proxy_map(boost::param_not_found) const {}
@@ -1923,7 +1923,7 @@ private:
 
   /*!
    * @brief checks if a vertex is attached with an anchor.
-   * @tparam VertexAnchorIndexMap `WritablePropertyMap`
+   * @tparam VertexAnchorIndexMap `ReadablePropertyMap`
    * with `boost::graph_traights<TriangleMesh>::vertex_descriptor` as key and `std::size_t` as value type
    * @param vtx a vertex descriptor
    * @param vanchor_map vertex anchor index map