diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/exact_inset.cpp b/Minkowski_sum_2/examples/Minkowski_sum_2/exact_inset.cpp
index fe72e22369f..938c116b8f8 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/exact_inset.cpp
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/exact_inset.cpp
@@ -21,7 +21,7 @@ int main()
 
 #include "arr_conics.h"
 
-typedef CGAL::Polygon_2<Rat_kernel>             Polygon;
+typedef CGAL::Polygon_2<Rat_kernel>             Polygon_2;
 typedef CGAL::Gps_traits_2<Traits>              Gps_traits;
 typedef Gps_traits::Polygon_2                   Offset_polygon;
 
@@ -34,7 +34,7 @@ int main(int argc, char* argv[])
     std::cerr << "Failed to open the input file." << std::endl;
     return -1;
   }
-  Polygon P;
+  Polygon_2 P;
   in_file >> P;
   in_file.close();
   std::cout << "Read an input polygon with " << P.size() << " vertices."
diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/exact_offset.cpp b/Minkowski_sum_2/examples/Minkowski_sum_2/exact_offset.cpp
index 0e5e731036d..cef25bb7d4e 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/exact_offset.cpp
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/exact_offset.cpp
@@ -21,9 +21,9 @@ int main()
 
 #include "arr_conics.h"
 
-typedef CGAL::Polygon_2<Rat_kernel>             Polygon;
+typedef CGAL::Polygon_2<Rat_kernel>             Polygon_2;
 typedef CGAL::Gps_traits_2<Traits>              Gps_traits;
-typedef Gps_traits::Polygon_with_holes_2        Offset_polygon_with_holes;
+typedef Gps_traits::Polygon_with_holes_2        Offset_polygon_with_holes_2;
 
 int main(int argc, char* argv[])
 {
@@ -34,7 +34,7 @@ int main(int argc, char* argv[])
     std::cerr << "Failed to open the input file." << std::endl;
     return -1;
   }
-  Polygon  P;
+  Polygon_2  P;
   in_file >> P;
   in_file.close();
   std::cout << "Read an input polygon with " << P.size() << " vertices."
@@ -43,7 +43,7 @@ int main(int argc, char* argv[])
   // Compute the offset polygon.
   Traits traits;
   boost::timer timer;
-  Offset_polygon_with_holes offset = CGAL::offset_polygon_2(P, 5, traits);
+  Offset_polygon_with_holes_2 offset = CGAL::offset_polygon_2(P, 5, traits);
   double secs = timer.elapsed();
 
   std::cout << "The offset polygon has " << offset.outer_boundary().size()
diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/pgn_print.h b/Minkowski_sum_2/examples/Minkowski_sum_2/pgn_print.h
index 3bdcf0edca3..3ac462ac4fc 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/pgn_print.h
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/pgn_print.h
@@ -9,10 +9,10 @@
 //-----------------------------------------------------------------------------
 // Pretty-print a CGAL polygon.
 //
-template <typename Polygon> void print_polygon(const Polygon & pgn)
+template <typename Polygon_2> void print_polygon(const Polygon_2 & pgn)
 {
   std::cout << "[ " << pgn.size() << " vertices: (";
-  typename Polygon::Vertex_const_iterator  vit;
+  typename Polygon_2::Vertex_const_iterator  vit;
   for (vit = pgn.vertices_begin(); vit != pgn.vertices_end(); ++vit)
     std::cout << "(" << *vit << ')';
   std::cout << ") ]" << std::endl;
diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/sum_by_decomposition.cpp b/Minkowski_sum_2/examples/Minkowski_sum_2/sum_by_decomposition.cpp
index c09523c039f..6c4fd6aa745 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/sum_by_decomposition.cpp
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/sum_by_decomposition.cpp
@@ -12,8 +12,8 @@
 
 typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
 typedef Kernel::Point_2                                   Point;
-typedef CGAL::Polygon_2<Kernel>                           Polygon;
-typedef CGAL::Polygon_with_holes_2<Kernel>                Polygon_with_holes;
+typedef CGAL::Polygon_2<Kernel>                           Polygon_2;
+typedef CGAL::Polygon_with_holes_2<Kernel>                Polygon_with_holes_2;
 
 int main(int argc, char* argv[])
 {
@@ -24,13 +24,13 @@ int main(int argc, char* argv[])
     std::cerr << "Failed to open the input file." << std::endl;
     return -1;
   }
-  Polygon   P, Q;
+  Polygon_2   P, Q;
   in_file >> P >> Q;
   in_file.close();
 
   // Compute the Minkowski sum using the decomposition approach.
   CGAL::Small_side_angle_bisector_decomposition_2<Kernel>  ssab_decomp;
-  Polygon_with_holes  sum = CGAL::minkowski_sum_2(P, Q, ssab_decomp);
+  Polygon_with_holes_2  sum = CGAL::minkowski_sum_2(P, Q, ssab_decomp);
   std::cout << "P (+) Q = "; print_polygon_with_holes(sum);
   return 0;
 }
diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h
index 125fbf58588..46af3d93baf 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h
@@ -324,7 +324,7 @@ private:
   }
 
   // Returns a sorted list of the polygon's edges
-  std::vector<Direction_2> directions_of_polygon(const Polygon_2& p,
+  std::vector<Direction_2> directions_of_polygon(
     const std::vector<Point_2>& points) const
   {
     std::vector<Direction_2> directions;