diff --git a/include/boost/geometry/algorithms/detail/overlay/assemble.hpp b/include/boost/geometry/algorithms/detail/overlay/assemble.hpp
index 3a7e0af21..413402423 100644
--- a/include/boost/geometry/algorithms/detail/overlay/assemble.hpp
+++ b/include/boost/geometry/algorithms/detail/overlay/assemble.hpp
@@ -14,6 +14,7 @@
 #include <vector>
 
 #include <boost/range.hpp>
+#include <boost/mpl/assert.hpp>
 
 
 #include <boost/geometry/algorithms/detail/overlay/turn_info.hpp>
@@ -162,7 +163,13 @@ struct convert_ring<polygon_tag>
 
 template <typename Tag, typename Geometry>
 struct add_to_containment
-{};
+{
+    BOOST_MPL_ASSERT_MSG
+        (
+            false, NOT_OR_NOT_YET_IMPLEMENTED_FOR_THIS_GEOMETRY_TYPE
+            , (types<Geometry>)
+        );
+};
 
 template <typename Ring>
 struct add_to_containment<ring_tag, Ring>
diff --git a/include/boost/geometry/algorithms/intersection.hpp b/include/boost/geometry/algorithms/intersection.hpp
index a2a4c408e..b2af587f9 100644
--- a/include/boost/geometry/algorithms/intersection.hpp
+++ b/include/boost/geometry/algorithms/intersection.hpp
@@ -13,6 +13,7 @@
 #include <cstddef>
 
 #include <boost/mpl/if.hpp>
+#include <boost/mpl/assert.hpp>
 #include <boost/range/metafunctions.hpp>
 
 
@@ -118,8 +119,48 @@ template
     typename Strategy
 >
 struct intersection_inserter
-    : detail::overlay::overlay
-        <Geometry1, Geometry2, OutputIterator, GeometryOut, -1, Strategy>
+{
+    BOOST_MPL_ASSERT_MSG
+        (
+            false, NOT_OR_NOT_YET_IMPLEMENTED_FOR_THIS_GEOMETRY_TYPES
+            , (types<Geometry1, Geometry2, GeometryOut>)
+        );
+};
+
+
+template
+<
+    typename Polygon1, typename Polygon2,
+    typename OutputIterator,
+    typename PolygonOut,
+    typename Strategy
+>
+struct intersection_inserter
+    <
+        polygon_tag, polygon_tag, polygon_tag,
+        Polygon1, Polygon2,
+        OutputIterator, PolygonOut,
+        Strategy
+    > : detail::overlay::overlay
+        <Polygon1, Polygon2, OutputIterator, PolygonOut, -1, Strategy>
+{};
+
+
+template
+<
+    typename Polygon, typename Box,
+    typename OutputIterator,
+    typename PolygonOut,
+    typename Strategy
+>
+struct intersection_inserter
+    <
+        polygon_tag, box_tag, polygon_tag,
+        Polygon, Box,
+        OutputIterator, PolygonOut,
+        Strategy
+    > : detail::overlay::overlay
+        <Polygon, Box, OutputIterator, PolygonOut, -1, Strategy>
 {};
 
 
diff --git a/include/boost/geometry/multi/algorithms/intersection.hpp b/include/boost/geometry/multi/algorithms/intersection.hpp
index 1eebc356b..e214d245d 100644
--- a/include/boost/geometry/multi/algorithms/intersection.hpp
+++ b/include/boost/geometry/multi/algorithms/intersection.hpp
@@ -21,8 +21,41 @@ namespace boost { namespace geometry
 namespace dispatch
 {
 
-// Currently empty, all done in overlay / assemble
 
+template
+<
+    typename Polygon, typename MultiPolygon,
+    typename OutputIterator,
+    typename PolygonOut,
+    typename Strategy
+>
+struct intersection_inserter
+    <
+        polygon_tag, multi_polygon_tag, polygon_tag,
+        Polygon, MultiPolygon,
+        OutputIterator, PolygonOut,
+        Strategy
+    > : detail::overlay::overlay
+        <Polygon, MultiPolygon, OutputIterator, PolygonOut, -1, Strategy>
+{};
+
+
+template
+<
+    typename MultiPolygon1, typename MultiPolygon2,
+    typename OutputIterator,
+    typename PolygonOut,
+    typename Strategy
+>
+struct intersection_inserter
+    <
+        multi_polygon_tag, multi_polygon_tag, polygon_tag,
+        MultiPolygon1, MultiPolygon2,
+        OutputIterator, PolygonOut,
+        Strategy
+    > : detail::overlay::overlay
+        <MultiPolygon1, MultiPolygon2, OutputIterator, PolygonOut, -1, Strategy>
+{};
 
 
 } // namespace dispatch