diff --git a/include/boost/geometry/algorithms/detail/buffer/buffered_piece_collection.hpp b/include/boost/geometry/algorithms/detail/buffer/buffered_piece_collection.hpp
index 2039c1bd0..e657ff978 100644
--- a/include/boost/geometry/algorithms/detail/buffer/buffered_piece_collection.hpp
+++ b/include/boost/geometry/algorithms/detail/buffer/buffered_piece_collection.hpp
@@ -826,7 +826,7 @@ struct buffered_piece_collection
             selected[id] = properties(*it, true);
         }
 
-        detail::overlay::assign_parents(offsetted_rings, traversed_rings, selected, false);
+        detail::overlay::assign_parents(offsetted_rings, traversed_rings, selected, true);
         return detail::overlay::add_rings<GeometryOutput>(selected, offsetted_rings, traversed_rings, out);
     }
 
diff --git a/include/boost/geometry/algorithms/detail/overlay/assign_parents.hpp b/include/boost/geometry/algorithms/detail/overlay/assign_parents.hpp
index a7cbd038d..67b48cc47 100644
--- a/include/boost/geometry/algorithms/detail/overlay/assign_parents.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/assign_parents.hpp
@@ -127,30 +127,30 @@ struct assign_visitor
     template <typename Item>
     inline void apply(Item const& outer, Item const& inner, bool first = true)
     {
-        if (first && outer.real_area < 0)
+        if (first && outer.abs_area < inner.abs_area)
         {
-            // Reverse arguments
+            // Apply with reversed arguments
             apply(inner, outer, false);
             return;
         }
 
-        if (math::larger(outer.real_area, 0))
+        if (m_check_for_orientation
+         || (math::larger(outer.real_area, 0)
+          && math::smaller(inner.real_area, 0)))
         {
-            if (inner.real_area < 0 || m_check_for_orientation)
-            {
-                ring_info_type& inner_in_map = m_ring_map[inner.id];
+            ring_info_type& inner_in_map = m_ring_map[inner.id];
 
-                if (geometry::within(inner_in_map.point, outer.envelope)
-                   && within_selected_input(inner_in_map, outer.id, m_geometry1, m_geometry2, m_collection)
-                   )
+            if (geometry::within(inner_in_map.point, outer.envelope)
+               && within_selected_input(inner_in_map, outer.id, m_geometry1, m_geometry2, m_collection)
+               )
+            {
+                // Assign a parent if there was no earlier parent, or the newly
+                // found parent is smaller than the previous one
+                if (inner_in_map.parent.source_index == -1
+                    || outer.abs_area < inner_in_map.parent_area)
                 {
-                    // Only assign parent if that parent is smaller (or if it is the first)
-                    if (inner_in_map.parent.source_index == -1
-                        || outer.abs_area < inner_in_map.parent_area)
-                    {
-                        inner_in_map.parent = outer.id;
-                        inner_in_map.parent_area = outer.abs_area;
-                    }
+                    inner_in_map.parent = outer.id;
+                    inner_in_map.parent_area = outer.abs_area;
                 }
             }
         }
@@ -288,13 +288,21 @@ inline void assign_parents(Geometry1 const& geometry1,
             {
                 it->second.discarded = true;
             }
-            else if (it->second.parent.source_index >= 0 && it->second.get_area() > 0)
+            else if (it->second.parent.source_index >= 0
+                    && math::larger(it->second.get_area(), 0))
             {
-                // Discard positive inner ring with parent
-                it->second.discarded = true;
+                const ring_info_type& parent = ring_map[it->second.parent];
+
+                if (math::larger(parent.area, 0))
+                {
+                    // Discard positive inner ring with positive parent
+                    it->second.discarded = true;
+                }
+                // Remove parent ID from any positive inner ring
                 it->second.parent.source_index = -1;
             }
-            else if (it->second.parent.source_index < 0 && it->second.get_area() < 0)
+            else if (it->second.parent.source_index < 0
+                    && math::smaller(it->second.get_area(), 0))
             {
                 // Reverse negative ring without parent
                 it->second.reversed = true;
@@ -313,6 +321,8 @@ inline void assign_parents(Geometry1 const& geometry1,
     }
 }
 
+
+// Version for one geometry (called by buffer)
 template
 <
     typename Geometry,
@@ -324,7 +334,7 @@ inline void assign_parents(Geometry const& geometry,
             RingMap& ring_map,
             bool check_for_orientation)
 {
-    // Call it with an empty geometry
+    // Call it with an empty geometry as second geometry (source_id == 1)
     // (ring_map should be empty for source_id==1)
 
     Geometry empty;
diff --git a/test/algorithms/buffer/linestring_buffer.cpp b/test/algorithms/buffer/linestring_buffer.cpp
index eaff55e67..bdca6e3d0 100644
--- a/test/algorithms/buffer/linestring_buffer.cpp
+++ b/test/algorithms/buffer/linestring_buffer.cpp
@@ -64,9 +64,9 @@ void test_all()
     //    test_one<linestring, polygon>("simplex_asym_neg", simplex, join_miter, end_round, 3.202, +1.5, -1.0);
     //    test_one<linestring, polygon>("simplex_asym_pos", simplex, join_miter, end_round, 3.202, -1.0, +1.5);
 
-    // Generates a reverse polygon, with a negative area, which will be made empty TODO decide about this
-    test_one<linestring, polygon>("simplex_asym_neg_rev", simplex, join_miter, end_flat, 0, +1.0, -1.5);
-    test_one<linestring, polygon>("simplex_asym_pos_rev", simplex, join_miter, end_flat, 0, -1.5, +1.0);
+    // Generates (initially) a reversed polygon, with a negative area, which is reversed afterwards in assign_parents
+    test_one<linestring, polygon>("simplex_asym_neg_rev", simplex, join_miter, end_flat, 3.202, +1.0, -1.5);
+    test_one<linestring, polygon>("simplex_asym_pos_rev", simplex, join_miter, end_flat, 3.202, -1.5, +1.0);
 
     test_one<linestring, polygon>("straight", straight, join_round, end_flat, 38.4187, 1.5, 1.5);
     test_one<linestring, polygon>("straight", straight, join_miter, end_flat, 38.4187, 1.5, 1.5);
diff --git a/test/algorithms/buffer/multi_polygon_buffer.cpp b/test/algorithms/buffer/multi_polygon_buffer.cpp
index 5fa0a3a68..5001b8ef7 100644
--- a/test/algorithms/buffer/multi_polygon_buffer.cpp
+++ b/test/algorithms/buffer/multi_polygon_buffer.cpp
@@ -217,7 +217,12 @@ static std::string const rt_s2
 static std::string const rt_t
     = "MULTIPOLYGON(((1 3,1 4,2 3,1 3)),((1 4,0 3,0 4,0 5,1 4)))";
 
+// Creates traversed ring
+static std::string const rt_u1
+    = "MULTIPOLYGON(((7 6,8 7,8 6,7 6)),((8 9,9 10,9 9,8 9)),((2 8,3 9,3 8,2 8)),((6 5,6 6,7 6,6 5)),((6 7,7 7,6 6,5 6,6 7)),((7 7,7 8,8 7,7 7)),((6 7,6 8,7 8,6 7)),((8 7,8 8,9 8,9 7,8 7)))";
 
+static std::string const rt_u2
+    = "MULTIPOLYGON(((4 2,5 3,5 2,4 2)),((6 4,6 5,7 5,6 4)),((7 4,7 5,8 5,7 4)),((7 3,7 4,8 3,7 3)),((7 10,8 10,7 9,6 9,7 10)),((0 7,0 8,1 7,0 7)),((6 1,6 2,7 2,7 1,6 1)),((5 7,5 8,6 9,6 8,7 9,7 8,7 7,6 6,6 7,5 7)),((5 4,6 4,6 3,5 3,4 3,4 4,5 4)),((5 2,6 2,5 1,4 0,3 0,4 1,3 1,3 2,3 3,4 3,4 2,4.5 1.5,5 2)),((5 6,5 5,4 5,4 6,4 7,5 7,5 6)),((5 0,5 1,5.5 0.5,6 1,6 0,5 0)),((5 9,5 8,4 8,3 8,2 8,1 8,0 8,1 9,1 10,2 9,2 10,3 10,4 10,5 10,5 9)),((4 5,4 4,3 4,3 3,2 3,1 3,0 3,0 4,0 5,0 6,1 6,2 5,1 5,1 4,2 4,3 5,2 5,2 6,2.5 5.5,3 6,4 5)),((3 2,2 2,2 3,3 2)),((2 0,1 0,2 1,3 0,2 0)),((1 1,0 1,0 2,0 3,1 2,1.5 1.5,2 2,3 1,2 1,1 1)),((2 6,1 6,1 7,2 7,3 7,2 6)),((4 8,4 7,3 7,4 8)),((9 6,8 6,7 6,7 7,8 7,8.5 6.5,9 7,8 7,8 8,8.5 7.5,9 8,8 8,8 9,9 9,9 10,10 10,10 9,10 8,10 7,10 6,10 5,9 4,9 5,8 5,9 6)),((7 0,6 0,7 1,8 1,7 0)),((8 3,9 2,8 2,7 2,8 3)),((10 2,10 1,10 0,9 0,9 1,8 1,8 2,8.5 1.5,9 2,9 3,10 4,10 3,10 2)),((9 4,9 3,8 3,8 4,9 4)))";
 
 
 template <typename P>
@@ -336,8 +341,10 @@ void test_all()
     test_one<multi_polygon_type, polygon_type>("rt_s1", rt_s1, join_miter, end_flat, 20.4853, 1.0);
     test_one<multi_polygon_type, polygon_type>("rt_s2", rt_s2, join_miter, end_flat, 24.6495, 1.0);
     test_one<multi_polygon_type, polygon_type>("rt_t", rt_t, join_miter, end_flat, 15.6569, 1.0);
-}
 
+    test_one<multi_polygon_type, polygon_type>("rt_u1", rt_u1, join_round, end_flat, 33.2032, 1.0);
+    test_one<multi_polygon_type, polygon_type>("rt_u2", rt_u2, join_round, end_flat, 138.8001, 1.0);
+}
 
 int test_main(int, char* [])
 {