diff --git a/include/boost/geometry/algorithms/detail/overlay/enrich_intersection_points.hpp b/include/boost/geometry/algorithms/detail/overlay/enrich_intersection_points.hpp
index b8e17b357..bd2552193 100644
--- a/include/boost/geometry/algorithms/detail/overlay/enrich_intersection_points.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/enrich_intersection_points.hpp
@@ -27,9 +27,9 @@
 
 #include <boost/geometry/algorithms/detail/ring_identifier.hpp>
 #include <boost/geometry/algorithms/detail/overlay/copy_segment_point.hpp>
-#include <boost/geometry/algorithms/detail/overlay/get_relative_order.hpp>
 #include <boost/geometry/algorithms/detail/overlay/handle_tangencies.hpp>
 #include <boost/geometry/policies/robustness/robust_type.hpp>
+#include <boost/geometry/strategies/side.hpp>
 #ifdef BOOST_GEOMETRY_DEBUG_ENRICH
 #  include <boost/geometry/algorithms/detail/overlay/check_enrich.hpp>
 #endif
@@ -152,12 +152,26 @@ private :
     {
         robust_point_type pi, pj, ri, rj, si, sj;
         get_situation_map(left, right, pi, pj, ri, rj, si, sj);
-        int const order = get_relative_order
+
+        typedef typename strategy::side::services::default_strategy
             <
-                robust_point_type
-            >::apply(pi, pj, ri, rj, si, sj);
-        //debug("r/o", order == -1);
-        return order == -1;
+                typename cs_tag<point_type>::type
+            >::type strategy;
+        int const side_rj_p = strategy::apply(pi, pj, rj);
+        int const side_sj_p = strategy::apply(pi, pj, sj);
+
+        // Put the one turning left (1; right == -1) as last
+        if (side_rj_p != side_sj_p)
+        {
+            return side_rj_p < side_sj_p;
+        }
+
+        int const side_sj_r = strategy::apply(ri, rj, sj);
+        int const side_rj_s = strategy::apply(si, sj, rj);
+
+        // If they both turn left: the most left as last
+        // If they both turn right: this is not relevant, but take also here most left
+        return side_rj_s < side_sj_r;
     }
 
 public :
@@ -176,9 +190,6 @@ public :
             {
                 // First check "real" intersection (crosses)
                 // -> distance zero due to precision, solve it by sorting
-                // TODO: reconsider this. Using integer maths, this will
-                // ALWAYS return 0 because either fractions are different, or
-                // the (currently calculated) relative-order is identical
                 if (m_turn_points[left.turn_index].method == method_crosses
                     && m_turn_points[right.turn_index].method == method_crosses)
                 {
diff --git a/test/algorithms/buffer/multi_polygon_buffer.cpp b/test/algorithms/buffer/multi_polygon_buffer.cpp
index c86c75a6a..90b5c40b7 100644
--- a/test/algorithms/buffer/multi_polygon_buffer.cpp
+++ b/test/algorithms/buffer/multi_polygon_buffer.cpp
@@ -236,7 +236,6 @@ static std::string const rt_u6
 // For this case (and more), get_left_turns or using a more specific sort order is essential
 static std::string const rt_u7
     = "MULTIPOLYGON(((4 5,4 6,5 5,4 5)),((9 2,9 3,10 3,10 2,9 2)),((7 3,7 4,8 4,8 3,7 3)),((5 5,6 6,6 5,5 5)),((3 6,4 7,4 6,3 6)),((0 5,0 6,1 5,0 5)))";
-  //  = "MULTIPOLYGON(((4 5,4 6,5 5,4 5)),((9 2,9 3,10 3,10 2,9 2)),((7 3,7 4,8 4,8 3,7 3)),((5 5,6 6,6 5,5 5)),((3 6,4 7,4 6,3 6)))"; //removing the leftmost uninvolved polygon solves somehow the problem...
 
 template <typename P>
 void test_all()
@@ -246,6 +245,7 @@ void test_all()
 
     bg::strategy::buffer::join_miter join_miter;
     bg::strategy::buffer::join_round join_round(100);
+    bg::strategy::buffer::join_round join_round_rough(12);
     bg::strategy::buffer::end_flat end_flat;
 
     test_one<multi_polygon_type, polygon_type>("triangles424", triangles, join_miter, end_flat, 417.910, 4.24);
@@ -353,12 +353,10 @@ void test_all()
     test_one<multi_polygon_type, polygon_type>("rt_u4", rt_u4, join_round, end_flat, 126.9268, 1.0);
     test_one<multi_polygon_type, polygon_type>("rt_u5", rt_u5, join_round, end_flat, 78.4906, 1.0);
     test_one<multi_polygon_type, polygon_type>("rt_u6", rt_u6, join_round, end_flat, 115.4461, 1.0);
-#if defined(BOOST_GEOMETRY_BUFFER_INCLUDE_FAILING_TESTS)
-    {
-        bg::strategy::buffer::join_round join_round_rough(12); // temporary
-        test_one<multi_polygon_type, polygon_type>("rt_u7", rt_u7, join_round_rough, end_flat, 999, 1.0);
-    }
-#endif
+
+    test_one<multi_polygon_type, polygon_type>("rt_u7", rt_u7, join_round, end_flat, 35.6233, 1.0);
+    test_one<multi_polygon_type, polygon_type>("rt_u7", rt_u7, join_miter, end_flat, 42.6421, 1.0);
+    test_one<multi_polygon_type, polygon_type>("rt_u7_rough", rt_u7, join_round_rough, end_flat, 35.0483, 1.0);
 }
 
 int test_main(int, char* [])