diff --git a/doc/release_notes.qbk b/doc/release_notes.qbk
index 22b1a9642..70c726f54 100644
--- a/doc/release_notes.qbk
+++ b/doc/release_notes.qbk
@@ -23,7 +23,8 @@
 
 * The support of parameters convertible to value_type in rtree insert(), remove() and count() functions
 * Support for counterclockwise input/output in algorithm buffer
-* Support for degenerate input in algorithm buffer
+* Support for open-geometry input in algorithm buffer (open output not yet supported)
+* Support for degenerate input (point-like linestrings, polygons) in algorithm buffer
 
 [*Solved tickets]
 
diff --git a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
index 2021a0481..c959ee849 100644
--- a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
+++ b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
@@ -16,6 +16,7 @@
 
 #include <boost/range.hpp>
 
+#include <boost/geometry/core/closure.hpp>
 #include <boost/geometry/core/exterior_ring.hpp>
 #include <boost/geometry/core/interior_rings.hpp>
 
@@ -513,7 +514,12 @@ struct buffer_inserter<ring_tag, RingInput, RingOutput>
         bool has_output = false;
 
         std::size_t n = boost::size(simplified);
-        if (n > 3)
+        std::size_t const min_points = core_detail::closure::minimum_ring_size
+            <
+                geometry::closure<RingInput>::value
+            >::value;
+
+        if (n >= min_points)
         {
             detail::normalized_view<RingInput const> view(simplified);
             if (distance.negative())
diff --git a/test/algorithms/buffer/polygon_buffer.cpp b/test/algorithms/buffer/polygon_buffer.cpp
index fe3e48bf5..f4cee670f 100644
--- a/test/algorithms/buffer/polygon_buffer.cpp
+++ b/test/algorithms/buffer/polygon_buffer.cpp
@@ -388,9 +388,12 @@ void test_mixed()
     bg::strategy::buffer::end_flat end_flat;
 
     std::ostringstream name;
-    name << "mixed_" << std::boolalpha << InputClockwise << "_" << OutputClockwise << "_" << InputClosed << "_" << OutputClosed;
+    name << "mixed_" << std::boolalpha
+        << InputClockwise << "_" << OutputClockwise
+        << "_" << InputClosed << "_" << OutputClosed;
 
-    test_one<input_polygon_type, output_polygon_type>(name.str(), simplex, join_round, end_flat, 47.4831, 1.5);
+    test_one<input_polygon_type, output_polygon_type>(name.str(),
+            simplex, join_round, end_flat, 47.4831, 1.5);
 }
 
 #ifdef HAVE_TTMATH
@@ -402,13 +405,25 @@ int test_main(int, char* [])
     typedef bg::model::point<double, 2, bg::cs::cartesian> dpoint;
 
     test_all<true, dpoint>();
+
+#if ! defined(BOOST_GEOMETRY_TEST_ONLY_ONE_TYPE)
     test_all<false, dpoint>();
-    //test_all<bg::model::point<tt, 2, bg::cs::cartesian> >();
 
     test_mixed<dpoint, dpoint, false, false, true, true>();
     test_mixed<dpoint, dpoint, false, true, true, true>();
     test_mixed<dpoint, dpoint, true, false, true, true>();
     test_mixed<dpoint, dpoint, true, true, true, true>();
 
+    test_mixed<dpoint, dpoint, false, false, false, true>();
+    test_mixed<dpoint, dpoint, false, true, false, true>();
+    test_mixed<dpoint, dpoint, true, false, false, true>();
+    test_mixed<dpoint, dpoint, true, true, false, true>();
+
+#ifdef HAVE_TTMATH
+    test_all<bg::model::point<tt, 2, bg::cs::cartesian> >();
+#endif
+
+#endif
+
     return 0;
 }