diff --git a/include/boost/geometry/algorithms/detail/overlay/add_rings.hpp b/include/boost/geometry/algorithms/detail/overlay/add_rings.hpp
index 74595fedd..5ff0b57d6 100644
--- a/include/boost/geometry/algorithms/detail/overlay/add_rings.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/add_rings.hpp
@@ -75,15 +75,15 @@ inline OutputIterator add_rings(SelectionMap const& map,
             OutputIterator out)
 {
     typedef typename SelectionMap::const_iterator iterator;
-	typedef typename SelectionMap::mapped_type property_type;
-	typedef typename property_type::area_type area_type;
+    typedef typename SelectionMap::mapped_type property_type;
+    typedef typename property_type::area_type area_type;
 
-	area_type const zero = 0;
-	std::size_t const min_num_points = core_detail::closure::minimum_ring_size
-		<
-			geometry::closure
-				<
-					typename boost::range_value
+    area_type const zero = 0;
+    std::size_t const min_num_points = core_detail::closure::minimum_ring_size
+        <
+            geometry::closure
+                <
+                    typename boost::range_value
                         <
                             RingCollection const
                         >::type
@@ -117,15 +117,14 @@ inline OutputIterator add_rings(SelectionMap const& map,
                 }
             }
 
-			// Only add rings if they satisfy minimal requirements.
-			// This cannot be done earlier (during traversal), not
-			// everything is figured out yet (sum of positive/negative rings)
-			// TODO: individual rings can still contain less than 3 points.
-			if (geometry::num_points(result) >= min_num_points
-				&& math::larger(geometry::area(result), zero))
-			{
-				*out++ = result;
-			}
+            // Only add rings if they satisfy minimal requirements.
+            // This cannot be done earlier (during traversal), not
+            // everything is figured out yet (sum of positive/negative rings)
+            if (geometry::num_points(result) >= min_num_points
+                && math::larger(geometry::area(result), zero))
+            {
+                *out++ = result;
+            }
         }
     }
     return out;
diff --git a/include/boost/geometry/algorithms/detail/overlay/convert_ring.hpp b/include/boost/geometry/algorithms/detail/overlay/convert_ring.hpp
index 05bd721e7..ae86fb1d9 100644
--- a/include/boost/geometry/algorithms/detail/overlay/convert_ring.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/convert_ring.hpp
@@ -77,12 +77,23 @@ struct convert_ring<polygon_tag>
         }
         else
         {
-            interior_rings(destination).resize(
-                        interior_rings(destination).size() + 1);
-            geometry::convert(source, interior_rings(destination).back());
-            if (reverse)
+            // Avoid adding interior rings which are invalid because of number of points:
+            if (geometry::num_points(source) >=
+                    core_detail::closure::minimum_ring_size
+                        <
+                            geometry::closure
+                                <
+                                    Destination
+                                >::value
+                        >::value)
             {
-                boost::reverse(interior_rings(destination).back());
+                interior_rings(destination).resize(
+                            interior_rings(destination).size() + 1);
+                geometry::convert(source, interior_rings(destination).back());
+                if (reverse)
+                {
+                    boost::reverse(interior_rings(destination).back());
+                }
             }
         }
     }