diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
index 36b93215109..255cfa3a6e9 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h
@@ -40,7 +40,7 @@ void compute_statistics(const Triangulation& tr,
   typedef typename Tr::Cell_handle   Cell_handle;
   typedef typename Tr::Vertex_handle Vertex_handle;
   typedef typename Gt::Point_3       Point;
-  typedef typename Tr::Finite_facets_iterator Finite_facets_iterator;
+  typedef typename Tr::Facet         Facet;
   typedef typename Tr::Finite_cells_iterator  Finite_cells_iterator;
   typedef typename Tr::Cell::Subdomain_index  Subdomain_index;
 
@@ -58,11 +58,10 @@ void compute_statistics(const Triangulation& tr,
   double max_dihedral_angle = 0.;
   double min_dihedral_angle = 180.;
 
-  for (Finite_facets_iterator fit = tr.finite_facets_begin();
-       fit != tr.finite_facets_end(); ++fit)
+  for (Facet fit : tr.finite_facets())
   {
-    const Cell_handle cell = fit->first;
-    const int& index = fit->second;
+    const Cell_handle cell = fit.first;
+    const int& index = fit.second;
     if (!cell_selector(cell) || !cell_selector(cell->neighbor(index)))
       continue;
 
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
index 7c784af9820..3adb0ffe080 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
@@ -379,15 +379,13 @@ private:
     boost::unordered_map<Vertex_handle,
     std::vector<Surface_patch_index> >& vertices_surface_indices)
   {
-    for (typename C3t3::Facets_in_complex_iterator
-         fit = c3t3.facets_in_complex_begin();
-         fit != c3t3.facets_in_complex_end(); ++fit)
+    for (Facet fit : c3t3.facets_in_complex())
     {
-      const Surface_patch_index& surface_index = c3t3.surface_patch_index(*fit);
+      const Surface_patch_index& surface_index = c3t3.surface_patch_index(fit);
 
       for (int i = 0; i < 3; i++)
       {
-        const Vertex_handle vi = fit->first->vertex(indices(fit->second, i));
+        const Vertex_handle vi = fit.first->vertex(indices(fit.second, i));
 
         std::vector<Surface_patch_index>& v_surface_indices = vertices_surface_indices[vi];
         if (std::find(v_surface_indices.begin(), v_surface_indices.end(), surface_index) == v_surface_indices.end())
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
index d0d3c12f442..cb636c6b7a0 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/split_long_edges.h
@@ -238,7 +238,6 @@ void split_long_edges(C3T3& c3t3,
   typedef typename C3T3::Triangulation       T3;
   typedef typename T3::Cell_handle           Cell_handle;
   typedef typename T3::Edge                  Edge;
-  typedef typename T3::Finite_edges_iterator Finite_edges_iterator;
   typedef typename T3::Vertex_handle         Vertex_handle;
   typedef typename std::pair<Vertex_handle, Vertex_handle> Edge_vv;
 
@@ -259,10 +258,8 @@ void split_long_edges(C3T3& c3t3,
   //collect long edges
   T3& tr = c3t3.triangulation();
   Boost_bimap long_edges;
-  for (Finite_edges_iterator eit = tr.finite_edges_begin();
-       eit != tr.finite_edges_end(); ++eit)
+  for (Edge e : tr.finite_edges())
   {
-    Edge e = *eit;
     if (!can_be_split(e, c3t3, protect_boundaries, cell_selector))
       continue;