diff --git a/doc/release_notes.qbk b/doc/release_notes.qbk
index 249510236..5ccdcd5f7 100644
--- a/doc/release_notes.qbk
+++ b/doc/release_notes.qbk
@@ -27,6 +27,7 @@
 * [@https://svn.boost.org/trac/boost/ticket/9245 9245] Check for process errors in make_qbk.py
 * [@https://svn.boost.org/trac/boost/ticket/9081 9081] Booleans create self-intersecting polygons from non-self-intersecting polygons
 * [@https://svn.boost.org/trac/boost/ticket/8310 8310] Wrong results with overlapping polygons (fixed using point_on_surface for disjoint)
+* [@https://svn.boost.org/trac/boost/ticket/9871 9871] Remove spike in polygon with only a spike
 
 [*Bugfixes]
 
diff --git a/include/boost/geometry/algorithms/remove_spikes.hpp b/include/boost/geometry/algorithms/remove_spikes.hpp
index 634391b64..62845135f 100644
--- a/include/boost/geometry/algorithms/remove_spikes.hpp
+++ b/include/boost/geometry/algorithms/remove_spikes.hpp
@@ -69,7 +69,7 @@ struct range_remove_spikes
         std::size_t const min_num_points = core_detail::closure::minimum_ring_size
             <
                 geometry::closure<Range>::value
-            >::value;
+            >::value - 1; // subtract one: a polygon with only one spike should result into one point
         if (n < min_num_points)
         {
             return;
@@ -104,13 +104,13 @@ struct range_remove_spikes
             found = false;
             // Check for spike in first point
             int const penultimate = 2;
-            while(cleaned.size() > 3 && detail::point_is_spike_or_equal(cleaned.front(), *(cleaned.end() - penultimate), cleaned.back()))
+            while(cleaned.size() >= 3 && detail::point_is_spike_or_equal(cleaned.front(), *(cleaned.end() - penultimate), cleaned.back()))
             {
                 cleaned.pop_back();
                 found = true;
             }
             // Check for spike in second point
-            while(cleaned.size() > 3 && detail::point_is_spike_or_equal(*(cleaned.begin() + 1), cleaned.back(), cleaned.front()))
+            while(cleaned.size() >= 3 && detail::point_is_spike_or_equal(*(cleaned.begin() + 1), cleaned.back(), cleaned.front()))
             {
                 cleaned.pop_front();
                 found = true;
@@ -118,6 +118,13 @@ struct range_remove_spikes
         }
         while (found);
 
+        if (cleaned.size() == 2)
+        {
+            // Ticket #9871: open polygon with only two points.
+            // the second point forms, by definition, a spike
+            cleaned.pop_back();
+        }
+
         // Close if necessary
         if (geometry::closure<Range>::value == geometry::closed)
         {
diff --git a/test/algorithms/remove_spikes.cpp b/test/algorithms/remove_spikes.cpp
index 97552e570..2545e10ba 100644
--- a/test/algorithms/remove_spikes.cpp
+++ b/test/algorithms/remove_spikes.cpp
@@ -134,6 +134,32 @@ void test_polygons()
     test_geometry<polygon>("spike_with_corner",
             "POLYGON((0 0,0 4,4 4,4 2,6 2,6 4,6 2,4 2,4 0,0 0))",
             16, 16);
+
+    test_geometry<polygon>("triangle0",
+            "POLYGON((0 0,0 4,2 0,4 0,0 0))",
+            4, 6 + sqrt(20.0));
+    test_geometry<polygon>("triangle1",
+            "POLYGON((0 4,2 0,4 0,0 0,0 4))",
+            4, 6 + sqrt(20.0));
+    test_geometry<polygon>("triangle2",
+            "POLYGON((2 0,4 0,0 0,0 4,2 0))",
+            4, 6 + sqrt(20.0));
+    test_geometry<polygon>("triangle3",
+            "POLYGON((4 0,0 0,0 4,2 0,4 0))",
+            4, 6 + sqrt(20.0));
+
+    test_geometry<polygon>("only_spike1",
+            "POLYGON((0 0,2 2,0 0))",
+            0, 0);
+    test_geometry<polygon>("only_spike2",
+            "POLYGON((0 0,2 2,4 4,2 2,0 0))",
+            0, 0);
+    test_geometry<polygon>("only_spike3",
+            "POLYGON((0 0,2 2,4 4,0 0))",
+            0, 0);
+    test_geometry<polygon>("only_spike4",
+            "POLYGON((0 0,4 4,2 2,0 0))",
+            0, 0);
 }