diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Hole_filter_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Hole_filter_2.h
new file mode 100644
index 00000000000..4f472fddd73
--- /dev/null
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Hole_filter_2.h
@@ -0,0 +1,57 @@
+#ifndef CGAL_MINKOWSKI_SUM_HOLE_FILTER_2_H
+#define CGAL_MINKOWSKI_SUM_HOLE_FILTER_2_H
+
+#include <CGAL/basic.h>
+#include <vector>
+
+namespace CGAL {
+
+template <class Kernel_, class Container_>
+class Hole_filter_2
+{
+
+private:
+
+  typedef Kernel_ Kernel;
+  typedef Container_ Container;
+
+  typedef CGAL::Polygon_with_holes_2<Kernel, Container> Polygon_with_holes_2;
+
+public:
+
+  void operator()(const Polygon_with_holes_2 &pgn1, const Polygon_with_holes_2 &pgn2,
+                  Polygon_with_holes_2 &filtered_pgn1) const
+  {
+    filtered_pgn1 = pgn1;
+
+    Bbox_2 boundary_bbox;
+    typename Polygon_with_holes_2::Hole_iterator it;
+
+    std::vector<typename Polygon_with_holes_2::Hole_iterator> to_erase;
+    boundary_bbox = pgn2.outer_boundary().bbox();
+
+    it = filtered_pgn1.holes_begin();
+    while (it != filtered_pgn1.holes_end())
+    {
+      Bbox_2 hole_bbox = (*it).bbox();
+
+      if (hole_bbox.ymax()-hole_bbox.ymin() < boundary_bbox.ymax()-boundary_bbox.ymin() ||
+          hole_bbox.xmax()-hole_bbox.xmin() < boundary_bbox.xmax()-boundary_bbox.xmin())
+      {
+        to_erase.push_back(it);
+      }
+      ++it;
+    }
+
+    typename std::vector<typename Polygon_with_holes_2::Hole_iterator>::iterator it2 = to_erase.begin();
+    while (it2 != to_erase.end())
+    {
+      filtered_pgn1.erase_hole(*it2);
+      ++it2;
+    }
+  }
+};
+
+} // namespace CGAL
+
+#endif
diff --git a/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h b/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
index 78dcdcb715c..c06013e3fc2 100644
--- a/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
+++ b/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
@@ -21,6 +21,7 @@
 #include <CGAL/basic.h>
 #include <CGAL/Polygon_with_holes_2.h>
 
+#include <CGAL/Minkowski_sum_2/Hole_filter_2.h>
 #include <CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h>
 #include <CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h>
 #include <CGAL/Minkowski_sum_2/Minkowski_sum_decomp_2.h>
@@ -79,11 +80,19 @@ minkowski_sum_reduced_convolution_2(const Polygon_with_holes_2<Kernel_, Containe
   typedef Kernel_                                    Kernel;
   typedef Container_                                 Container;
 
+  Hole_filter_2<Kernel, Container> hole_filter;
+
+  Polygon_with_holes_2<Kernel,Container> filtered_pgn1;
+  Polygon_with_holes_2<Kernel,Container> filtered_pgn2;
+
+  hole_filter(pgn1, pgn2, filtered_pgn1);
+  hole_filter(pgn2, pgn1, filtered_pgn2);
+
   Minkowski_sum_by_reduced_convolution_2<Kernel, Container> mink_sum;
   Polygon_2<Kernel,Container>                               sum_bound;
   std::list<Polygon_2<Kernel,Container> >                   sum_holes;
 
-  mink_sum (pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
+  mink_sum (filtered_pgn1, filtered_pgn2, sum_bound, std::back_inserter(sum_holes));
 
   return (Polygon_with_holes_2<Kernel,Container> (sum_bound,
                                                   sum_holes.begin(),
@@ -252,7 +261,16 @@ minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
 {
   typename Minkowski_sum_by_decomposition_2<DecompositionStrategy_,
                                             Container_>::Traits_2 traits;
-  return minkowski_sum_2(pgn1, pgn2, decomposition_strategy, traits);
+
+  Hole_filter_2<Kernel_, Container_> hole_filter;
+
+  Polygon_with_holes_2<Kernel_,Container_> filtered_pgn1;
+  Polygon_with_holes_2<Kernel_,Container_> filtered_pgn2;
+
+  hole_filter(pgn1, pgn2, filtered_pgn1);
+  hole_filter(pgn2, pgn1, filtered_pgn2);
+
+  return minkowski_sum_2(filtered_pgn1, filtered_pgn2, decomposition_strategy, traits);
 }
 
 /*!
@@ -282,7 +300,16 @@ minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
 
   Minkowski_sum_by_decomposition_2<Decomposition_strategy, Container>
     mink_sum(decomposition_strategy, traits);
-  Polygon_with_holes_2<Kernel, Container> sum = mink_sum(pgn1, pgn2);
+
+  Hole_filter_2<Kernel_, Container_> hole_filter;
+
+  Polygon_with_holes_2<Kernel_,Container_> filtered_pgn1;
+  Polygon_with_holes_2<Kernel_,Container_> filtered_pgn2;
+
+  hole_filter(pgn1, pgn2, filtered_pgn1);
+  hole_filter(pgn2, pgn1, filtered_pgn2);
+
+  Polygon_with_holes_2<Kernel, Container> sum = mink_sum(filtered_pgn1, filtered_pgn2);
   return sum;
 }
 
@@ -305,6 +332,9 @@ minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
 {
   typename Minkowski_sum_by_decomposition_2<DecompositionStrategy_,
                                             Container_>::Traits_2 traits;
+
+  // TODO: Apply Hole_filter_2
+
   return minkowski_sum_2(pgn1, pgn2, decomposition_strategy, traits);
 }
 
@@ -335,6 +365,9 @@ minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
 
   Minkowski_sum_by_decomposition_2<Decomposition_strategy, Container>
     mink_sum(decomposition_strategy, traits);
+
+  // TODO: Apply Hole_filter_2
+
   Polygon_with_holes_2<Kernel, Container> sum = mink_sum(pgn1, pgn2);
   return sum;
 }