diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index 16e355c20e4..16e9918519e 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -128,6 +128,8 @@ public:
   typedef typename Tds::Halfedge_iterator      All_halfedges_iterator;
   typedef typename Tds::Vertex_iterator        All_vertices_iterator;
 
+  typedef typename Gt::Construct_point_2       Construct_point_2;
+
   class Perturbation_order
   {
     const Self *t;
@@ -277,7 +279,9 @@ public:
                Face_handle &fr) const;
 
   // GEOMETRIC FEATURES AND CONSTRUCTION
-  Point_2 construct_point(const Point& p) const;
+  typename boost::result_of<const Construct_point_2(const Point&)>::type
+  construct_point(const Point& p) const { return geom_traits().construct_point_2_object()(p); }
+
   const Point& point(Face_handle c, int i) const;
   const Point& point(Vertex_handle v) const;
   Segment segment(Face_handle f, int i) const;
@@ -595,7 +599,6 @@ std::ptrdiff_t insert(InputIterator first, InputIterator last)
 
   std::vector<Point> points (first, last);
 
-  typedef typename Geom_traits::Construct_point_2 Construct_point_2;
   typedef typename boost::result_of<const Construct_point_2(const Point&)>::type Ret;
   typedef CGAL::internal::boost_::function_property_map<Construct_point_2, Point, Ret> fpmap;
   typedef CGAL::Spatial_sort_traits_adapter_2<Geom_traits, fpmap> Search_traits_2;
@@ -967,14 +970,6 @@ is_face(Vertex_handle v1,
   return _tds.is_face(v1, v2, v3, fr);
 }
 
-template <class Gt, class Tds >
-typename Triangulation_2<Gt, Tds>::Point_2
-Triangulation_2<Gt, Tds>::
-construct_point(const Point& p) const
-{
-  return geom_traits().construct_point_2_object()(p);
-}
-
 template <class Gt, class Tds >
 const typename Triangulation_2<Gt, Tds>::Point&
 Triangulation_2<Gt, Tds>::
diff --git a/Triangulation_3/include/CGAL/Triangulation_3.h b/Triangulation_3/include/CGAL/Triangulation_3.h
index 2e3771adad4..ebe2a7de594 100644
--- a/Triangulation_3/include/CGAL/Triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Triangulation_3.h
@@ -433,6 +433,8 @@ public:
 
   typedef typename Tds::Simplex                Simplex;
 
+  typedef typename GT::Construct_point_3       Construct_point_3;
+
 private:
   // This class is used to generate the Finite_*_iterators.
   class Infinite_tester
@@ -553,7 +555,8 @@ protected:
 
 public:
   template<typename P> // Point or Point_3
-  Point_3 construct_point(const P& p) const
+  typename boost::result_of<const Construct_point_3(const P&)>::type
+  construct_point(const P& p) const
   {
     return geom_traits().construct_point_3_object()(p);
   }
@@ -1127,7 +1130,6 @@ public:
     // Nevertheless, to make it more generic (that is, allowing the user to pass
     // a `Point` type that is not GT::Point_3), we still use the spatial sort
     // adapter traits and Construct_point_3 here.
-    typedef typename Geom_traits::Construct_point_3 Construct_point_3;
     typedef typename boost::result_of<const Construct_point_3(const Point&)>::type Ret;
     typedef CGAL::internal::boost_::function_property_map<Construct_point_3, Point, Ret> fpmap;
     typedef CGAL::Spatial_sort_traits_adapter_3<Geom_traits, fpmap> Search_traits_3;