diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index 5702d0173..49ab9e133 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -96,6 +96,7 @@ _remove_invalid_gids (hb_set_t *glyphs,
 static hb_set_t *
 _populate_gids_to_retain (hb_face_t *face,
 			  const hb_set_t *unicodes,
+                          const hb_set_t *input_glyphs_to_retain,
 			  bool close_over_gsub,
 			  hb_set_t *unicodes_to_retain,
 			  hb_map_t *codepoint_to_glyph,
@@ -110,6 +111,7 @@ _populate_gids_to_retain (hb_face_t *face,
 
   hb_set_t *initial_gids_to_retain = hb_set_create ();
   initial_gids_to_retain->add (0); // Not-def
+  hb_set_union (initial_gids_to_retain, input_glyphs_to_retain);
 
   hb_codepoint_t cp = HB_SET_VALUE_INVALID;
   while (unicodes->next (&cp))
@@ -213,6 +215,7 @@ hb_subset_plan_create (hb_face_t           *face,
   plan->reverse_glyph_map = hb_map_create();
   plan->_glyphset = _populate_gids_to_retain (face,
                                               input->unicodes,
+                                              input->glyphs,
                                               !plan->drop_layout,
                                               plan->unicodes,
                                               plan->codepoint_to_glyph,
diff --git a/test/api/hb-subset-test.h b/test/api/hb-subset-test.h
index cefa4e066..3e759a8a9 100644
--- a/test/api/hb-subset-test.h
+++ b/test/api/hb-subset-test.h
@@ -48,7 +48,7 @@ typedef short bool;
 HB_BEGIN_DECLS
 
 static inline hb_subset_input_t *
-hb_subset_test_create_input(const hb_set_t  *codepoints)
+hb_subset_test_create_input (const hb_set_t *codepoints)
 {
   hb_subset_input_t *input = hb_subset_input_create_or_fail ();
   hb_set_t * input_codepoints = hb_subset_input_unicode_set (input);
@@ -56,6 +56,15 @@ hb_subset_test_create_input(const hb_set_t  *codepoints)
   return input;
 }
 
+static inline hb_subset_input_t *
+hb_subset_test_create_input_from_glyphs (const hb_set_t *glyphs)
+{
+  hb_subset_input_t *input = hb_subset_input_create_or_fail ();
+  hb_set_t * input_glyphs  = hb_subset_input_glyph_set (input);
+  hb_set_union (input_glyphs, glyphs);
+  return input;
+}
+
 static inline hb_face_t *
 hb_subset_test_create_subset (hb_face_t *source,
                               hb_subset_input_t *input)
diff --git a/test/api/test-subset-glyf.c b/test/api/test-subset-glyf.c
index e8609ca83..4671156f9 100644
--- a/test/api/test-subset-glyf.c
+++ b/test/api/test-subset-glyf.c
@@ -79,6 +79,29 @@ test_subset_glyf (void)
   hb_face_destroy (face_ac);
 }
 
+static void
+test_subset_glyf_with_input_glyphs (void)
+{
+  hb_face_t *face_abc = hb_test_open_font_file ("fonts/Roboto-Regular.abc.ttf");
+  hb_face_t *face_ac = hb_test_open_font_file ("fonts/Roboto-Regular.ac.ttf");
+
+  hb_set_t *glyphs = hb_set_create();
+  hb_face_t *face_abc_subset;
+  hb_set_add (glyphs, 1);
+  hb_set_add (glyphs, 3);
+  face_abc_subset =
+      hb_subset_test_create_subset (face_abc, hb_subset_test_create_input_from_glyphs (glyphs));
+  hb_set_destroy (glyphs);
+
+  hb_subset_test_check (face_ac, face_abc_subset, HB_TAG ('g','l','y','f'));
+  hb_subset_test_check (face_ac, face_abc_subset, HB_TAG ('l','o','c', 'a'));
+  check_maxp_num_glyphs(face_abc_subset, 3, true);
+
+  hb_face_destroy (face_abc_subset);
+  hb_face_destroy (face_abc);
+  hb_face_destroy (face_ac);
+}
+
 static void
 test_subset_glyf_with_components (void)
 {
@@ -291,6 +314,7 @@ main (int argc, char **argv)
 
   hb_test_add (test_subset_glyf_noop);
   hb_test_add (test_subset_glyf);
+  hb_test_add (test_subset_glyf_with_input_glyphs);
   hb_test_add (test_subset_glyf_strip_hints_simple);
   hb_test_add (test_subset_glyf_strip_hints_composite);
   hb_test_add (test_subset_glyf_strip_hints_invalid);