diff --git a/Partition_2/include/CGAL/Partition_2/Rotation_tree_2.h b/Partition_2/include/CGAL/Partition_2/Rotation_tree_2.h
index 9aa9bc64067..1272820344d 100644
--- a/Partition_2/include/CGAL/Partition_2/Rotation_tree_2.h
+++ b/Partition_2/include/CGAL/Partition_2/Rotation_tree_2.h
@@ -53,7 +53,19 @@ public:
    typedef typename internal::vector<Node>::iterator  Self_iterator;
    typedef typename Traits::Point_2                Point_2;
 
-  using  internal::vector< Rotation_tree_node_2<Traits_> >::push_back;
+   using internal::vector< Rotation_tree_node_2<Traits_> >::push_back;
+
+   class Less {
+      typename Traits::Less_xy_2 less;
+      typedef typename Traits::Point_2 Point;
+   public:
+      Less(typename Traits::Less_xy_2 less) : less(less) {}
+
+      template <typename Point_like>
+      bool operator()(const Point_like& p1, const Point_like& p2) {
+         return less(Point(p1), Point(p2));
+      }
+   };
 
    // constructor
    template<class ForwardIterator>
@@ -61,9 +73,9 @@ public:
    {
       for (ForwardIterator it = first; it != beyond; it++)
          push_back(*it);
-   
-      std::sort(this->begin(), this->end(), 
-                boost::bind(Traits().less_xy_2_object(), _2, _1));
+
+      Less less (Traits().less_xy_2_object());
+      std::sort(this->begin(), this->end(), less);
       std::unique(this->begin(), this->end());
    
       // front() is the point with the largest x coordinate
@@ -166,3 +178,8 @@ private:
 #include <CGAL/Partition_2/Rotation_tree_2_impl.h>
 
 #endif // CGAL_ROTATION_TREE_H
+
+// For the Emacs editor:
+// Local Variables:
+// c-basic-offset: 3
+// End:
diff --git a/Partition_2/include/CGAL/Partition_2/Triangulation_indirect_traits_2.h b/Partition_2/include/CGAL/Partition_2/Triangulation_indirect_traits_2.h
index b21b7297346..6f9eaefdec4 100644
--- a/Partition_2/include/CGAL/Partition_2/Triangulation_indirect_traits_2.h
+++ b/Partition_2/include/CGAL/Partition_2/Triangulation_indirect_traits_2.h
@@ -57,9 +57,11 @@ private:
    Circulator _p0, _p1, _p2;
 };
 
-template <class Compare_x_2>
+template <class Traits>
 class Indirect_compare_x_2
 {
+   typedef typename Traits::Compare_x_2 Compare_x_2;
+   typedef typename Traits::Point_2     Point;
 public:
    Indirect_compare_x_2(const Compare_x_2& compare_x_2)
      : _compare_x_2(compare_x_2)
@@ -68,16 +70,18 @@ public:
    template <class Point_2_ptr>
    Comparison_result operator()(Point_2_ptr p1, Point_2_ptr p2)
    {
-      return _compare_x_2(*p1, *p2);
+      return _compare_x_2(Point(*p1), Point(*p2));
    }
 
 private:
    Compare_x_2 _compare_x_2;
 };
 
-template <class Compare_y_2>
+template <class Traits>
 class Indirect_compare_y_2
 {
+   typedef typename Traits::Compare_y_2 Compare_y_2;
+   typedef typename Traits::Point_2     Point;
 public:
    Indirect_compare_y_2(const Compare_y_2& compare_y_2)
      : _compare_y_2(compare_y_2)
@@ -86,16 +90,18 @@ public:
    template <class Point_2_ptr>
    Comparison_result operator()(Point_2_ptr p1, Point_2_ptr p2)
    {
-      return _compare_y_2(*p1, *p2);
+      return _compare_y_2(Point(*p1), Point(*p2));
    }
 
 private:
    Compare_y_2 _compare_y_2;
 };
 
-template <class Orientation_2>
+template <class Traits>
 class Indirect_orientation_2
 {
+   typedef typename Traits::Orientation_2 Orientation_2;
+   typedef typename Traits::Point_2 Point;
 public:
    Indirect_orientation_2(const Orientation_2& orientation_2)
      : _orientation_2(orientation_2)
@@ -104,7 +110,7 @@ public:
    template <class Point_2_ptr>
    Orientation operator()(Point_2_ptr p1, Point_2_ptr p2, Point_2_ptr p3)
    {
-      return _orientation_2(*p1, *p2, *p3);
+      return _orientation_2(Point(*p1), Point(*p2), Point(*p3));
    }
 
 private:
@@ -139,9 +145,9 @@ public:
   typedef Indirect_segment<Circulator>    Segment_2;
   typedef Indirect_triangle<Circulator>   Triangle_2;
 
-  typedef Indirect_orientation_2<typename Traits::Orientation_2> Orientation_2;
-  typedef Indirect_compare_x_2<typename Traits::Compare_x_2>     Compare_x_2;
-  typedef Indirect_compare_y_2<typename Traits::Compare_y_2>     Compare_y_2;
+  typedef Indirect_orientation_2<Traits>  Orientation_2;
+  typedef Indirect_compare_x_2<Traits>    Compare_x_2;
+  typedef Indirect_compare_y_2<Traits>    Compare_y_2;
   typedef Construct_indirect_segment_2<Circulator>      Construct_segment_2;
   typedef Construct_circulator_2<Circulator>            Construct_point_2;
 
@@ -181,3 +187,8 @@ private:
 }
 
 #endif // CGAL_TRIANGULATION_INDIRECT_TRAITS_2_H
+
+// For the Emacs editor
+// Local Variables:
+// c-basic-offset: 3
+// End:
diff --git a/Partition_2/include/CGAL/Partition_2/Vertex_visibility_graph_2_impl.h b/Partition_2/include/CGAL/Partition_2/Vertex_visibility_graph_2_impl.h
index c063270016e..82f95f7d4ee 100644
--- a/Partition_2/include/CGAL/Partition_2/Vertex_visibility_graph_2_impl.h
+++ b/Partition_2/include/CGAL/Partition_2/Vertex_visibility_graph_2_impl.h
@@ -227,20 +227,21 @@ Vertex_visibility_graph_2<Traits>::left_turn_to_parent(
                                    Tree_iterator q, 
                                    Tree& tree)
 {
+   typedef typename Traits::Point_2 Point;
    if (tree.parent_is_p_infinity(q)) 
    {
-      return (less_xy_2(*p, *q));
+      return (less_xy_2(Point(*p), Point(*q)));
    }
-   else if (orientation_2(*p, *q, *(*q).parent()) == COLLINEAR &&
-            (collinear_ordered_2(*p, *q, *(*q).parent()) ||
-             collinear_ordered_2(*p, *q, *(*q).parent())))
+   else if (orientation_2(Point(*p), Point(*q), Point(*q->parent())) == COLLINEAR &&
+            (collinear_ordered_2(Point(*p), Point(*q), Point(*q->parent())) ||
+             collinear_ordered_2(Point(*p), Point(*q), Point(*q->parent()))))
       
    {
       return true;
    }
    else
    {
-      return left_turn_2(*p, *q, *(*q).parent());
+      return left_turn_2(Point(*p), Point(*q), Point(*q->parent()));
    }
 }
 
diff --git a/Polygon/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h b/Polygon/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h
index 2ae98e403cc..96f42c39127 100644
--- a/Polygon/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h
+++ b/Polygon/include/CGAL/Polygon_2/Polygon_2_algorithms_impl.h
@@ -52,6 +52,25 @@ bool is_simple_2(ForwardIterator first,
     return is_simple_polygon(first, last, traits);
 }
 
+namespace internal { namespace Polygon_2 {
+
+template <typename Traits>
+class Compare_vertices {
+    typedef typename Traits::Less_xy_2 Less_xy_2;
+    typedef typename Traits::Point_2 Point_2;
+    Less_xy_2 less;
+public:
+    Compare_vertices(Less_xy_2 less) : less(less) {}
+
+    // `Point_like` derives from `Point_2`
+    template <typename Point_like>
+    bool operator()(const Point_like& p1, const Point_like& p2) {
+        return less(Point_2(p1), Point_2(p2));
+    }
+}; // end Compare_vertices
+
+} // end namespace Polygon_2
+} // end namespace internal
 
 //-----------------------------------------------------------------------//
 //                          left_vertex_2
@@ -64,7 +83,9 @@ ForwardIterator left_vertex_2(ForwardIterator first,
                                    const PolygonTraits&traits)
 {
     CGAL_polygon_precondition(first != last);
-    return std::min_element(first, last, traits.less_xy_2_object());
+    internal::Polygon_2::Compare_vertices<PolygonTraits>
+        less(traits.less_xy_2_object());
+    return std::min_element(first, last, less);
 }
 
 //-----------------------------------------------------------------------//
@@ -78,7 +99,9 @@ ForwardIterator right_vertex_2(ForwardIterator first,
                                     const PolygonTraits &traits)
 {
     CGAL_polygon_precondition(first != last);
-    return std::max_element(first, last, traits.less_xy_2_object());
+    internal::Polygon_2::Compare_vertices<PolygonTraits>
+        less(traits.less_xy_2_object());
+    return std::max_element(first, last, less);
 }
 
 //-----------------------------------------------------------------------//
@@ -423,3 +446,7 @@ Orientation orientation_2(ForwardIterator first,
 } //namespace CGAL
 
 /// \endcond
+
+// Local Variables:
+// c-basic-offset: 4
+// End: