diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
index 57edbcbe7fb..544a6a55e2d 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/IO/File_medit.h
@@ -89,7 +89,7 @@ void output_to_medit(std::ostream& os,
                      const Vertex_index_property_map& vertex_pmap,
                      const Facet_index_property_map& facet_pmap,
                      const Cell_index_property_map& cell_pmap,
-                     const Facet_index_property_map_twice& facet_twice_pmap = Facet_index_property_map_twice())
+                     const Facet_index_property_map_twice& = Facet_index_property_map_twice())
 {
 #ifdef CGAL_MESH_3_IO_VERBOSE
   std::cout << "Output to medit;\n"
@@ -119,7 +119,6 @@ void output_to_medit(std::ostream& os,
   typedef typename C3T3::Cell_handle             Cell_handle;
 
   typedef typename Tr::Vertex_iterator           Vertex_iterator;
-  typedef typename C3T3::Facet_iterator          Facet_iterator;
 
   typedef typename Tr::Offset                    Offset;
 
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
index 0c5dbc9a20b..58b2b7d5350 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_triangulation_3.h
@@ -955,7 +955,7 @@ public:
     typedef Cartesian_converter<EKernel, Kernel>                      Back_from_exact;
 
     typedef CGAL::Periodic_3_regular_triangulation_traits_3<EKernel>  Exact_Rt;
-    typedef typename Exact_Rt::Point_3                                EPoint_3;
+    typedef typename Exact_Rt::Weighted_point_3                       EWeighted_point_3;
 
     To_exact to_exact;
     Back_from_exact back_from_exact;
@@ -963,20 +963,17 @@ public:
     Exact_Rt etraits(to_exact(domain()));
     Exact_Rt::Construct_weighted_circumcenter_3 exact_weighted_circumcenter =
       etraits.construct_weighted_circumcenter_3_object();
-    Exact_Rt::Construct_point_3 exact_construct_point =
-      etraits.construct_point_3_object();
 
-    const typename Exact_Rt::Weighted_point_3& cp = to_exact(c->vertex((i+1)%4)->point());
-    const typename Exact_Rt::Weighted_point_3& cq = to_exact(c->vertex((i+2)%4)->point());
-    const typename Exact_Rt::Weighted_point_3& cr = to_exact(c->vertex((i+3)%4)->point());
-    const typename Exact_Rt::Weighted_point_3& cs = to_exact(ws);
+    const EWeighted_point_3& cp = to_exact(c->vertex((i+1)%4)->point());
+    const EWeighted_point_3& cq = to_exact(c->vertex((i+2)%4)->point());
+    const EWeighted_point_3& cr = to_exact(c->vertex((i+3)%4)->point());
+    const EWeighted_point_3& cs = to_exact(ws);
 
-    cc = back_from_exact(
-           exact_weighted_circumcenter(cp, cq, cr, cs,
-                                       pp_fcc.second + get_offset(c, (i+1)%4),
-                                       pp_fcc.second + get_offset(c, (i+2)%4),
-                                       pp_fcc.second + get_offset(c, (i+3)%4),
-                                       pp_s.second + min_off));
+    cc = back_from_exact(exact_weighted_circumcenter(cp, cq, cr, cs,
+                                                     pp_fcc.second + get_offset(c, (i+1)%4),
+                                                     pp_fcc.second + get_offset(c, (i+2)%4),
+                                                     pp_fcc.second + get_offset(c, (i+3)%4),
+                                                     pp_s.second + min_off));
   }
 
   void dual_segment(const Facet& facet, Bare_point& p, Bare_point& q) const
diff --git a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
index 5610bb0085f..dae35a7bec1 100644
--- a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
@@ -72,7 +72,6 @@ bool project_points(C3T3& c3t3,
                     InputIterator vertex_end)
 {
   typedef typename C3T3::Vertex_handle         Vertex_handle;
-  typedef typename C3T3::Cell_handle           Cell_handle;
 
   typedef typename C3T3::Triangulation         Tr;