diff --git a/include/boost/geometry/algorithms/detail/overlay/sort_by_side.hpp b/include/boost/geometry/algorithms/detail/overlay/sort_by_side.hpp
index 895652f89..78c168b5d 100644
--- a/include/boost/geometry/algorithms/detail/overlay/sort_by_side.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/sort_by_side.hpp
@@ -237,64 +237,6 @@ struct side_sorter
         }
     }
 
-    // Returns first index which is outgoing, and all incoming arcs are balanced
-    // by outgoing arcs
-    std::size_t first_open_index()
-    {
-        // map source index to state
-        typedef std::map<int, int> map_type;
-        map_type state;
-        bool free = false;
-        std::size_t result = m_ranked_points.size();
-        std::size_t last_main_rank = 0;
-
-        for (std::size_t i = 0; i < m_ranked_points.size(); i++)
-        {
-            const rp& ranked = m_ranked_points[i];
-
-            if (free && ranked.main_rank > last_main_rank)
-            {
-                return result;
-            }
-            free = false;
-
-            if (ranked.index == index_from)
-            {
-                state[ranked.seg_id.source_index]++;
-            }
-            else
-            {
-                state[ranked.seg_id.source_index]--;
-            }
-
-            if (ranked.index == index_to)
-            {
-                int sum = 0;
-                for (map_type::const_iterator it = state.begin();
-                     it != state.end(); ++it)
-                {
-                    sum += it->second;
-                }
-
-                if (sum == 0)
-                {
-                    // It is open. If next is a new main rank,
-                    // then this is the result
-                    free = true;
-                    result = i;
-                    last_main_rank = ranked.main_rank;
-                }
-            }
-        }
-
-        if (free)
-        {
-            return result;
-        }
-
-        return m_ranked_points.size();
-    }
-
     template <signed_size_type segment_identifier::*Member, typename Map>
     void find_open_generic(Map& handled)
     {
diff --git a/include/boost/geometry/algorithms/detail/overlay/traverse.hpp b/include/boost/geometry/algorithms/detail/overlay/traverse.hpp
index 0b1291e51..fedf06eb7 100644
--- a/include/boost/geometry/algorithms/detail/overlay/traverse.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/traverse.hpp
@@ -257,7 +257,7 @@ struct traversal
 
     inline bool select_from_cluster(signed_size_type& turn_index,
         int& op_index, signed_size_type start_turn_index,
-        sbs_type const& sbs)
+        sbs_type const& sbs, bool allow_pass_rank)
     {
         bool const is_union = OperationType == operation_union;
         bool const is_intersection = OperationType == operation_intersection;
@@ -314,7 +314,7 @@ struct traversal
                     result = true;
                     selected_rank = ranked_point.main_rank;
                 }
-                else
+                else if (! allow_pass_rank)
                 {
                     return result;
                 }
@@ -396,20 +396,10 @@ struct traversal
         if (open_count > 1)
         {
             sbs.reverse();
-
-            std::size_t index = sbs.first_open_index();
-            if (index < sbs.m_ranked_points.size())
-            {
-                typename sbs_type::rp const& ranked_point = sbs.m_ranked_points[index];
-                turn_index = ranked_point.turn_index;
-                op_index = ranked_point.op_index;
-                return true;
-            }
-            return false;
+            return select_from_cluster(turn_index, op_index, start_turn_index, sbs, true);
         }
 
-
-        return select_from_cluster(turn_index, op_index, start_turn_index, sbs);
+        return select_from_cluster(turn_index, op_index, start_turn_index, sbs, false);
     }
 
     inline void change_index_for_self_turn(signed_size_type& to_vertex_index,