diff --git a/include/boost/geometry/algorithms/detail/convex_hull/graham_andrew.hpp b/include/boost/geometry/algorithms/detail/convex_hull/graham_andrew.hpp
index 102318eeb..64d81054e 100644
--- a/include/boost/geometry/algorithms/detail/convex_hull/graham_andrew.hpp
+++ b/include/boost/geometry/algorithms/detail/convex_hull/graham_andrew.hpp
@@ -190,7 +190,7 @@ private:
 
         point_type most_left, most_right;
 
-        geometry::less<point_type, -1, Strategy> less;
+        geometry::less_exact<point_type, -1, Strategy> less;
 
         detail::convex_hull::get_extremes(in_proxy, most_left, most_right, less);
 
diff --git a/include/boost/geometry/policies/compare.hpp b/include/boost/geometry/policies/compare.hpp
index a5c8f0939..9dd8a694c 100644
--- a/include/boost/geometry/policies/compare.hpp
+++ b/include/boost/geometry/policies/compare.hpp
@@ -38,6 +38,29 @@ namespace boost { namespace geometry
     on equal x-es then on y, etc.
     If a dimension is specified, only that dimension is considered
 */
+
+template
+<
+    typename Point = void,
+    int Dimension = -1,
+    typename StrategyOrTag = void
+>
+struct less_exact
+{
+    using first_argument_type = Point;
+    using second_argument_type = Point;
+    using result_type = bool;
+
+    inline bool operator()(Point const& left, Point const& right) const
+    {
+        return StrategyOrTag::template compare_type
+            <
+                strategy::compare::less,
+                strategy::compare::equals_exact
+            >::apply(left, right);
+    }
+};
+
 template
 <
     typename Point = void,
@@ -54,7 +77,8 @@ struct less
     {
         return StrategyOrTag::template compare_type
             <
-                strategy::compare::less
+                strategy::compare::less,
+                strategy::compare::equals_epsilon
             >::apply(left, right);
     }
 };
@@ -91,7 +115,8 @@ struct less<void, Dimension, Strategy>
     {
         return Strategy::template compare_type
             <
-                strategy::compare::less
+                strategy::compare::less,
+                strategy::compare::equals_epsilon
             >::apply(left, right);
     }
 };
diff --git a/include/boost/geometry/strategies/convex_hull/cartesian.hpp b/include/boost/geometry/strategies/convex_hull/cartesian.hpp
index d61ace3c2..5bf46f211 100644
--- a/include/boost/geometry/strategies/convex_hull/cartesian.hpp
+++ b/include/boost/geometry/strategies/convex_hull/cartesian.hpp
@@ -50,11 +50,11 @@ public:
         return side_strategy_type();
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::cartesian
         <
             ComparePolicy,
-            strategy::compare::equals_exact,
+            EqualsPolicy,
             -1
         >;
 };
diff --git a/include/boost/geometry/strategies/convex_hull/geographic.hpp b/include/boost/geometry/strategies/convex_hull/geographic.hpp
index 4bcb53fd6..879d75284 100644
--- a/include/boost/geometry/strategies/convex_hull/geographic.hpp
+++ b/include/boost/geometry/strategies/convex_hull/geographic.hpp
@@ -65,11 +65,11 @@ public:
             >(base_t::m_spheroid);
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::spherical
         <
             ComparePolicy,
-            strategy::compare::equals_exact,
+            EqualsPolicy,
             -1
         >;
 };
diff --git a/include/boost/geometry/strategies/convex_hull/spherical.hpp b/include/boost/geometry/strategies/convex_hull/spherical.hpp
index 28262e292..6365b1c0f 100644
--- a/include/boost/geometry/strategies/convex_hull/spherical.hpp
+++ b/include/boost/geometry/strategies/convex_hull/spherical.hpp
@@ -47,11 +47,11 @@ public:
         return strategy::side::spherical_side_formula<CalculationType>();
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::spherical
         <
             ComparePolicy,
-            strategy::compare::equals_exact,
+            EqualsPolicy,
             -1
         >;
 };
diff --git a/include/boost/geometry/strategies/relate/cartesian.hpp b/include/boost/geometry/strategies/relate/cartesian.hpp
index 4ea0d7908..2b8a9e13a 100644
--- a/include/boost/geometry/strategies/relate/cartesian.hpp
+++ b/include/boost/geometry/strategies/relate/cartesian.hpp
@@ -189,11 +189,11 @@ public:
         return strategy::within::cartesian_box_box();
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::cartesian
         <
             ComparePolicy,
-            strategy::compare::equals_epsilon,
+            EqualsPolicy,
             -1
         >;
 };
diff --git a/include/boost/geometry/strategies/relate/geographic.hpp b/include/boost/geometry/strategies/relate/geographic.hpp
index c245ae530..b756f1a16 100644
--- a/include/boost/geometry/strategies/relate/geographic.hpp
+++ b/include/boost/geometry/strategies/relate/geographic.hpp
@@ -211,16 +211,13 @@ public:
         return strategy::within::spherical_box_box();
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::spherical
         <
             ComparePolicy,
-            strategy::compare::equals_epsilon,
+            EqualsPolicy,
             -1
         >;
-
-    //template <typename ComparePolicy, typename EqualsPolicy, int Dimension>
-    //using compare_type = strategy::compare::spherical<ComparePolicy, EqualsPolicy, Dimension>;
 };
 
 
@@ -293,12 +290,12 @@ struct strategy_converter<strategy::intersection::geographic_segments<FormulaPol
                 >(base_t::m_spheroid);
         }
 
-        template <typename ComparePolicy>
-        using compare_type = typename strategy::compare::cartesian
+        template <typename ComparePolicy, typename EqualsPolicy>
+        using compare_type = typename strategy::compare::spherical
             <
                 ComparePolicy,
-                strategy::compare::equals_epsilon,
-                -1
+                EqualsPolicy,
+               -1
             >;
     };
 
diff --git a/include/boost/geometry/strategies/relate/spherical.hpp b/include/boost/geometry/strategies/relate/spherical.hpp
index 22098d9f0..7914831fe 100644
--- a/include/boost/geometry/strategies/relate/spherical.hpp
+++ b/include/boost/geometry/strategies/relate/spherical.hpp
@@ -195,11 +195,11 @@ public:
         return strategy::within::spherical_box_box();
     }
 
-    template <typename ComparePolicy>
+    template <typename ComparePolicy, typename EqualsPolicy>
     using compare_type = typename strategy::compare::spherical
         <
             ComparePolicy,
-            strategy::compare::equals_epsilon,
+            EqualsPolicy,
             -1
         >;
 };