diff --git a/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h b/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
index 76266e19514..118e5ff5767 100644
--- a/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
@@ -90,6 +90,7 @@ public:
 
   typedef typename Tr_Base::All_cells_iterator       All_cells_iterator;
 
+  typedef typename Tr_Base::size_type size_type;
   typedef typename Tr_Base::Locate_type Locate_type;
 
 
@@ -206,7 +207,6 @@ public:
   insert(InputIterator first, InputIterator last)
   {
     size_type n = number_of_vertices();
-
     std::vector<Point> points (first, last);
     spatial_sort (points.begin(), points.end(), geom_traits());
 
diff --git a/Triangulation_3/include/CGAL/Regular_triangulation_3.h b/Triangulation_3/include/CGAL/Regular_triangulation_3.h
index 8adc8bf5ace..f62272b6531 100644
--- a/Triangulation_3/include/CGAL/Regular_triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Regular_triangulation_3.h
@@ -65,6 +65,7 @@ public:
   typedef typename Tr_Base::Facet               Facet;
   typedef typename Tr_Base::Edge                Edge;
 
+  typedef typename Tr_Base::size_type           size_type;
   typedef typename Tr_Base::Locate_type         Locate_type;
   typedef typename Tr_Base::Cell_iterator       Cell_iterator;
   typedef typename Tr_Base::Facet_iterator      Facet_iterator;
diff --git a/Triangulation_3/include/CGAL/Triangulation_3.h b/Triangulation_3/include/CGAL/Triangulation_3.h
index 7792282b4e2..0ff535881ad 100644
--- a/Triangulation_3/include/CGAL/Triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_3.h
@@ -1396,7 +1396,7 @@ operator<< (std::ostream& os, const Triangulation_3<GT, Tds> &tr)
   CGAL_triangulation_assertion( i == n+1 );
   CGAL_triangulation_assertion( tr.is_infinite(TV[0]) );
 
-  std::map<Vertex_handle, int > V;
+  std::map<Vertex_handle, std::size_t > V;
 
   V[tr.infinite_vertex()] = 0;
   for (i=1; i <= n; i++) {
diff --git a/Triangulation_3/include/CGAL/Triangulation_data_structure_3.h b/Triangulation_3/include/CGAL/Triangulation_data_structure_3.h
index b48ab130203..12c293eaa20 100644
--- a/Triangulation_3/include/CGAL/Triangulation_data_structure_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_data_structure_3.h
@@ -316,7 +316,7 @@ public:
 			   int & m, std::map< int, Cell_handle > &C );
   // not documented
   void print_cells(std::ostream& os,
-                   const std::map<Vertex_handle, int> &V ) const;
+                   const std::map<Vertex_handle, std::size_t> &V ) const;
 
   // ACCESS FUNCTIONS
 
@@ -1864,7 +1864,7 @@ read_cells(std::istream& is, std::map< int, Vertex_handle > &V,
 template < class Vb, class Cb>
 void
 Triangulation_data_structure_3<Vb,Cb>::
-print_cells(std::ostream& os, const std::map<Vertex_handle, int> &V ) const
+print_cells(std::ostream& os, const std::map<Vertex_handle, std::size_t> &V ) const
 {
   std::map<Cell_handle, int > C;
   int i = 0;