diff --git a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
index 7a901c869..1e2e6e33c 100644
--- a/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
+++ b/include/boost/geometry/algorithms/detail/buffer/buffer_inserter.hpp
@@ -345,6 +345,26 @@ struct visit_pieces_default_policy
     {}
 };
 
+template
+<
+    typename OutputPointType,
+    typename Point,
+    typename Collection,
+    typename DistanceStrategy,
+    typename PointStrategy
+>
+inline void buffer_point(Point const& point, Collection& collection,
+        DistanceStrategy const& distance_strategy,
+        PointStrategy const& point_strategy)
+{
+    collection.start_new_ring();
+    std::vector<OutputPointType> range_out;
+    point_strategy.apply(point, distance_strategy, range_out);
+    collection.add_piece(strategy::buffer::buffered_point, range_out, false);
+    collection.finish_ring();
+}
+
+
 }} // namespace detail::buffer
 #endif // DOXYGEN_NO_DETAIL
 
@@ -389,13 +409,10 @@ struct buffer_inserter<point_tag, Point, RingOutput>
             PointStrategy const& point_strategy,
             RobustPolicy const& )
     {
-        typedef typename point_type<RingOutput>::type output_point_type;
-
-        collection.start_new_ring();
-        std::vector<output_point_type> range_out;
-        point_strategy.apply(point, distance_strategy, range_out);
-        collection.add_piece(strategy::buffer::buffered_point, range_out, false);
-        collection.finish_ring();
+        detail::buffer::buffer_point
+        <
+            typename point_type<RingOutput>::type
+        >(point, collection, distance_strategy, point_strategy);
     }
 };
 
@@ -577,10 +594,11 @@ struct buffer_inserter<linestring_tag, Linestring, Polygon>
             SideStrategy const& side_strategy,
             JoinStrategy const& join_strategy,
             EndStrategy const& end_strategy,
-            PointStrategy const& ,
+            PointStrategy const& point_strategy,
             RobustPolicy const& robust_policy)
     {
-        if (boost::size(linestring) > 1)
+        std::size_t n = boost::size(linestring);
+        if (n > 1)
         {
             Linestring simplified;
             detail::buffer::simplify_input(linestring, distance, simplified);
@@ -598,9 +616,14 @@ struct buffer_inserter<linestring_tag, Linestring, Polygon>
                     first_p1);
             collection.finish_ring();
         }
-        else
+        else if (n == 1)
         {
             // Use point_strategy to buffer degenerated linestring
+            detail::buffer::buffer_point<output_point_type>
+                (
+                    geometry::range::front(linestring),
+                    collection, distance, point_strategy
+                );
         }
     }
 };
diff --git a/test/algorithms/buffer/linestring_buffer.cpp b/test/algorithms/buffer/linestring_buffer.cpp
index bdca6e3d0..8329d961f 100644
--- a/test/algorithms/buffer/linestring_buffer.cpp
+++ b/test/algorithms/buffer/linestring_buffer.cpp
@@ -27,6 +27,10 @@ static std::string const overlapping = "LINESTRING(0 0,4 5,7 4,10 6, 10 2,2 2)";
 static std::string const curve = "LINESTRING(2 7,3 5,5 4,7 5,8 7)";
 static std::string const tripod = "LINESTRING(5 0,5 5,1 8,5 5,9 8)"; // with spike
 
+static std::string const degenerate1 = "LINESTRING(5 5)";
+static std::string const degenerate2 = "LINESTRING(5 5,5 5)";
+static std::string const degenerate3 = "LINESTRING(5 5,5 5,5 5)";
+
 static std::string const for_collinear = "LINESTRING(2 0,0 0,0 4,6 4,6 0,4 0)";
 static std::string const for_collinear2 = "LINESTRING(2 1,2 0,0 0,0 4,6 4,6 0,4 0,4 1)";
 
@@ -133,6 +137,16 @@ void test_all()
     test_one<linestring, polygon>("field_sprayer1", field_sprayer1, join_round, end_round, 718.761877, 16.5, 6.5);
     test_one<linestring, polygon>("field_sprayer1", field_sprayer1, join_miter, end_round, 718.939628, 16.5, 6.5);
 
+    test_one<linestring, polygon>("degenerate1", degenerate1, join_round, end_round, 28.25, 3.0);
+#if defined(BOOST_GEOMETRY_BUFFER_INCLUDE_FAILING_TESTS)
+    test_one<linestring, polygon>("degenerate2", degenerate2, join_miter, end_flat, 99.99, 3.0);
+    test_one<linestring, polygon>("degenerate2", degenerate2, join_round, end_round, 99.99, 3.0);
+    test_one<linestring, polygon>("degenerate3", degenerate3, join_miter, end_flat, 99.99, 3.0);
+    test_one<linestring, polygon>("degenerate3", degenerate3, join_round, end_round, 99.99, 3.0);
+#endif
+
+
+
     double tolerance = 1.0e-10;
 
     test_one<linestring, polygon>("aimes120", aimes120, join_miter, end_flat, 1.62669948622351512e-08, 0.000018, 0.000018, false, tolerance);
diff --git a/test/algorithms/buffer/multi_linestring_buffer.cpp b/test/algorithms/buffer/multi_linestring_buffer.cpp
index 6174e3c8e..8d1481c47 100644
--- a/test/algorithms/buffer/multi_linestring_buffer.cpp
+++ b/test/algorithms/buffer/multi_linestring_buffer.cpp
@@ -15,6 +15,11 @@ static std::string const simplex = "MULTILINESTRING((0 0,4 5),(5 4,10 0))";
 static std::string const two_bends = "MULTILINESTRING((0 0,4 5,7 4,10 6),(1 5,5 9,8 6))";
 static std::string const turn_inside = "MULTILINESTRING((0 0,4 5,7 4,10 6),(1 5,5 9,8 6),(0 4,-2 6))";
 
+static std::string const degenerate0 = "MULTILINESTRING()";
+static std::string const degenerate1 = "MULTILINESTRING((5 5))";
+static std::string const degenerate2 = "MULTILINESTRING((5 5),(9 9))";
+static std::string const degenerate3 = "MULTILINESTRING((5 5),(9 9),(4 10))";
+
 
 template <typename P>
 void test_all()
@@ -49,6 +54,11 @@ void test_all()
     test_one<multi_linestring_type, polygon>("two_bends", two_bends, join_round_by_divide, end_flat, 64.6217, 1.5, 1.5);
     test_one<multi_linestring_type, polygon>("two_bends", two_bends, join_miter, end_flat, 65.1834, 1.5, 1.5);
     test_one<multi_linestring_type, polygon>("two_bends", two_bends, join_miter, end_round, 75.2917, 1.5, 1.5);
+
+    test_one<multi_linestring_type, polygon>("degenerate0", degenerate0, join_round, end_round, 0.0, 3.0, 3.0);
+    test_one<multi_linestring_type, polygon>("degenerate1", degenerate1, join_round, end_round, 28.2503, 3.0, 3.0);
+    test_one<multi_linestring_type, polygon>("degenerate2", degenerate2, join_round, end_round, 56.0457, 3.0, 3.0);
+    test_one<multi_linestring_type, polygon>("degenerate3", degenerate3, join_round, end_round, 80.4531, 3.0, 3.0);
 }