diff --git a/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h b/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
index 52551454373..497d9dcb2a2 100644
--- a/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
+++ b/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h
@@ -30,21 +30,49 @@
 
 namespace CGAL {
 
+/*!
+ * Computes the Minkowski sum \f$ P \oplus Q\f$ of the two given polygons.
+ * The function computes the reduced convolution of the two polygons and
+ * extracts those loops of the convolution which are part of the Minkowsi
+ * sum. This method works very efficiently, regardless of whether `P` and
+ * `Q` are convex or non-convex.
+ * Note that as the input polygons may not be convex, their Minkowski
+ * sum may not be a simple polygon. The result is therefore represented
+ * as a polygon with holes.
+ * \pre Both `P` and `Q` are simple, counterclockwise-oriented polygons.
+*/
+
+template <class Kernel, class Container>
+Polygon_with_holes_2<Kernel,Container>
+minkowski_sum_by_reduced_convolution_2 (const Polygon_2<Kernel,Container>& pgn1,
+                                        const Polygon_2<Kernel,Container>& 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;
+
+  if (pgn1.size() > pgn2.size())
+    mink_sum (pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
+  else
+    mink_sum (pgn2, pgn1, sum_bound, std::back_inserter(sum_holes));
+
+  return (Polygon_with_holes_2<Kernel,Container> (sum_bound,
+                                                  sum_holes.begin(),
+                                                  sum_holes.end()));
+}
+
 /*!
  * Compute the Minkowski sum of two simple polygons using the convolution
  * method.
  * Note that as the input polygons may not be convex, their Minkowski sum may
  * not be a simple polygon. The result is therefore represented as a polygon
  * with holes.
- * \param pgn1 The first polygon.
- * \param pgn2 The second polygon.
- * \return The resulting polygon with holes, representing the sum.
  */
 
 template <class Kernel, class Container>
 Polygon_with_holes_2<Kernel,Container>
-minkowski_sum_2 (const Polygon_2<Kernel,Container>& pgn1,
-                 const Polygon_2<Kernel,Container>& pgn2)
+minkowski_sum_by_full_convolution_2 (const Polygon_2<Kernel,Container>& pgn1,
+                                     const Polygon_2<Kernel,Container>& pgn2)
 {
   Minkowski_sum_by_convolution_2<Kernel, Container>  mink_sum;
   Polygon_2<Kernel,Container>                        sum_bound;
@@ -60,23 +88,23 @@ minkowski_sum_2 (const Polygon_2<Kernel,Container>& pgn1,
                                                   sum_holes.end()));
 }
 
+/*!
+ * Compute the Minkowski sum of two simple polygons using the reduced
+ * convolution method.
+ * Note that as the input polygons may not be convex, their Minkowski sum may
+ * not be a simple polygon. The result is therefore represented as a polygon
+ * with holes.
+ *
+ * \sa `CGAL::minkowski_sum_by_reduced_convolution_2()`
+ * \sa `CGAL::minkowski_sum_by_full_convolution_2()`
+ */
+
 template <class Kernel, class Container>
 Polygon_with_holes_2<Kernel,Container>
-minkowski_sum_2_new (const Polygon_2<Kernel,Container>& pgn1,
-                     const Polygon_2<Kernel,Container>& pgn2)
+minkowski_sum_2 (const Polygon_2<Kernel,Container>& pgn1,
+                 const Polygon_2<Kernel,Container>& 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;
-
-  if (pgn1.size() > pgn2.size())
-    mink_sum (pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
-  else
-    mink_sum (pgn2, pgn1, sum_bound, std::back_inserter(sum_holes));
-
-  return (Polygon_with_holes_2<Kernel,Container> (sum_bound,
-                                                  sum_holes.begin(),
-                                                  sum_holes.end()));
+  return minkowski_sum_by_reduced_convolution_2(pgn1, pgn2);
 }
 
 /*!
diff --git a/Minkowski_sum_2/test/Minkowski_sum_2/test_Minkowski_sum.cpp b/Minkowski_sum_2/test/Minkowski_sum_2/test_Minkowski_sum.cpp
index 1b32c75dcca..6cc34ffafb5 100644
--- a/Minkowski_sum_2/test/Minkowski_sum_2/test_Minkowski_sum.cpp
+++ b/Minkowski_sum_2/test/Minkowski_sum_2/test_Minkowski_sum.cpp
@@ -95,7 +95,7 @@ int main (int argc, char **argv)
     std::cout << "Using the reduced convolution method ... ";
     timer.reset();
     timer.start();
-    sum_conv_new = minkowski_sum_2_new (pgn1, pgn2);
+    sum_conv_new = minkowski_sum_by_reduced_convolution_2 (pgn1, pgn2);
     timer.stop();
     std::cout << "Done (" << timer.time() << " s)" << std::endl;
 
@@ -120,7 +120,7 @@ int main (int argc, char **argv)
     std::cout << "Using the convolution method ... ";
     timer.reset();
     timer.start();
-    sum_conv = minkowski_sum_2 (pgn1, pgn2);
+    sum_conv = minkowski_sum_by_full_convolution_2 (pgn1, pgn2);
     timer.stop();
     if (are_equal (result, sum_conv))
     {