diff --git a/Partition_2/doc/Partition_2/CGAL/Partition_traits_2.h b/Partition_2/doc/Partition_2/CGAL/Partition_traits_2.h
index ba6fef55ed5..b6113ea14f3 100644
--- a/Partition_2/doc/Partition_2/CGAL/Partition_traits_2.h
+++ b/Partition_2/doc/Partition_2/CGAL/Partition_traits_2.h
@@ -83,15 +83,11 @@ typedef R::Collinear_are_ordered_along_line_2 Collinear_are_ordered_along_line_2
 */ 
 typedef R::Are_strictly_ordered_along_line_2 Are_strictly_ordered_along_line_2; 
 
-/*!
-
-*/ 
-typedef CGAL::Polygon_traits_2<R> Poly_Traits; 
 
 /*!
 
 */ 
-typedef Poly_Traits::Point_2 Point_2; 
+typedef R::Point_2 Point_2; 
 
 /*!
 
@@ -101,7 +97,7 @@ typedef std::list<Point_2> Container;
 /*!
 
 */ 
-typedef CGAL::Polygon_2<Poly_Traits, Container> Polygon_2; 
+typedef CGAL::Polygon_2<R, Container> Polygon_2; 
 
 /*!
 
diff --git a/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp b/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
index 2036f194b8d..fe3cf534efe 100644
--- a/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
+++ b/Partition_2/examples/Partition_2/y_monotone_partition_indices_2.cpp
@@ -54,12 +54,11 @@ int main( )
       }
      std::cout << std::endl;
    }
-   
+
    assert(CGAL::partition_is_valid_2(polygon.vertices_begin(),
                                      polygon.vertices_end(),
                                      partition_polys.begin(),
                                      partition_polys.end(),
                                      traits));
-   
    return 0;
 }
diff --git a/Partition_2/include/CGAL/Partition_2/Partition_vertex_map.h b/Partition_2/include/CGAL/Partition_2/Partition_vertex_map.h
index cead0f87e9f..7990b51b94b 100644
--- a/Partition_2/include/CGAL/Partition_2/Partition_vertex_map.h
+++ b/Partition_2/include/CGAL/Partition_2/Partition_vertex_map.h
@@ -84,7 +84,7 @@ public:
   }
   
 private:
-  Traits_ traits;
+  const Traits_& traits;
 };
   
 template <class Traits_>
@@ -321,7 +321,7 @@ public:
   }
 
 private :
-  Traits traits;
+  const Traits& traits;
   List m_list ;
 };
 
@@ -532,7 +532,7 @@ private :
    }
 
 private :
-  Traits traits;
+  const Traits& traits;
   Map m_map ;
 };
 
diff --git a/Partition_2/include/CGAL/Partition_2/Partitioned_polygon_2.h b/Partition_2/include/CGAL/Partition_2/Partitioned_polygon_2.h
index fe2c9404433..50e21dd30e9 100644
--- a/Partition_2/include/CGAL/Partition_2/Partitioned_polygon_2.h
+++ b/Partition_2/include/CGAL/Partition_2/Partitioned_polygon_2.h
@@ -290,7 +290,7 @@ private:
    }
 
   Left_turn_2 _left_turn;
-  Traits traits;
+  const Traits& traits;
 };
 
 template <class Traits_>
diff --git a/Partition_2/include/CGAL/Partition_is_valid_traits_2.h b/Partition_2/include/CGAL/Partition_is_valid_traits_2.h
index b4c43eb8898..5d33a116b03 100644
--- a/Partition_2/include/CGAL/Partition_is_valid_traits_2.h
+++ b/Partition_2/include/CGAL/Partition_is_valid_traits_2.h
@@ -41,11 +41,11 @@ public:
 
   Partition_is_valid_traits_2()
   {}
-  
+
   Partition_is_valid_traits_2(const Traits& traits)
     : Traits(traits)
   {}
-  
+public:   
    Is_valid
    is_valid_object(const Traits& traits) const
    {  return Is_valid(traits); }
diff --git a/Partition_2/include/CGAL/Partition_traits_adapter_2.h b/Partition_2/include/CGAL/Partition_traits_adapter_2.h
index d4b79c96959..da3b7d77677 100644
--- a/Partition_2/include/CGAL/Partition_traits_adapter_2.h
+++ b/Partition_2/include/CGAL/Partition_traits_adapter_2.h
@@ -42,6 +42,7 @@ private:
   typedef Partition_traits_adapter_2<Base_traits,PointPropertyMap>       Self;
   
   PointPropertyMap ppmap;
+  
 public:
 
   Partition_traits_adapter_2(const Base_traits& base=Base_traits())
@@ -68,11 +69,11 @@ public:
     
     const PointPropertyMap& ppmap;
 
-    typename BaseFct::result_type operator()(Arg_type p, Arg_type q) const {
+    typename BaseFct::result_type operator()(const Arg_type& p, const Arg_type& q) const {
       return static_cast<const BaseFct*>(this)->operator()(get(ppmap,p),get(ppmap,q));
     }
     
-    typename BaseFct::result_type operator()(Arg_type p, Arg_type q, Arg_type r) const {
+    typename BaseFct::result_type operator()(const Arg_type& p, const Arg_type& q, const Arg_type& r) const {
       return static_cast<const BaseFct*>(this)->operator()(get(ppmap,p),get(ppmap,q),get(ppmap,r));
     }
   };
@@ -91,12 +92,6 @@ public:
     
     
     
-    typename K::Collinear_are_ordered_along_line_2::result_type
-    operator()(Arg_type p, Arg_type q, const typename K::Point_2& r) const
-    {
-      return fct(p.first, q.first, r);
-    }
-    
     typename K::Collinear_are_ordered_along_line_2::result_type
     operator()(Arg_type p, Arg_type q, Arg_type r) const
     {
diff --git a/Partition_2/include/CGAL/polygon_function_objects.h b/Partition_2/include/CGAL/polygon_function_objects.h
index 2de918623c6..b48ed8b70b2 100644
--- a/Partition_2/include/CGAL/polygon_function_objects.h
+++ b/Partition_2/include/CGAL/polygon_function_objects.h
@@ -47,28 +47,28 @@ template <class Traits>
 class Is_convex_2
 {
   public:
-     Is_convex_2(Traits t): traits(t) {}
+     Is_convex_2(const Traits& t): traits(t) {}
   
      template <class ForwardIterator>
      bool operator()(ForwardIterator first, ForwardIterator last)
      {  return is_convex_2(first, last, traits); }
 
   private:
-     Traits  traits;
+     const Traits& traits;
 };
 
 template <class Traits>
 class Is_y_monotone_2
 {
   public:
-     Is_y_monotone_2(Traits t): traits(t) {}
+     Is_y_monotone_2(const Traits& t): traits(t) {}
   
      template <class ForwardIterator>
      bool operator()(ForwardIterator first, ForwardIterator last)
      {  return is_y_monotone_2(first, last, traits); }
 
   private:
-     Traits  traits;
+     const Traits& traits;
 };
 
 }
diff --git a/Polygon/include/CGAL/Polygon_2.h b/Polygon/include/CGAL/Polygon_2.h
index deb45c86b89..612c4c1e945 100644
--- a/Polygon/include/CGAL/Polygon_2.h
+++ b/Polygon/include/CGAL/Polygon_2.h
@@ -147,7 +147,9 @@ class Polygon_2 {
     /// @{
 
     /// Creates an empty polygon.
-    Polygon_2(const Traits & p_traits = Traits()) : traits(p_traits) {}
+    Polygon_2() : traits() {}
+  
+    Polygon_2(const Traits & p_traits) : traits(p_traits) {}
 
     /// Copy constructor.
     Polygon_2(const Polygon_2<Traits_P,Container_P>& polygon)