diff --git a/src/hb-subset-input.cc b/src/hb-subset-input.cc
index 8a8b3f272..49fe7df21 100644
--- a/src/hb-subset-input.cc
+++ b/src/hb-subset-input.cc
@@ -547,13 +547,10 @@ HB_EXTERN void
 hb_subset_input_set_old_to_new_glyph_mapping (hb_subset_input_t *input,
                                               const hb_map_t* mapping)
 {
-  hb_set_t new_gids;
-  for (auto gid : mapping->values())
-  {
+  hb_set_t new_gids(mapping->values());
+  if (new_gids.get_population() != mapping->get_population())
     // Mapping cannot map multiple old gids to the same new gid.
-    if (new_gids.has(gid)) return;
-    new_gids.add(gid);
-  }
+    return;
 
   input->glyph_map = *mapping;
 }
diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index f018814e7..1e152d3e0 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -782,10 +782,16 @@ _create_old_gid_to_new_gid_map (const hb_face_t *face,
 
   if (*requested_glyph_map)
   {
-    hb_codepoint_t max_glyph = HB_SET_VALUE_INVALID;
+  
+    hb_codepoint_t max_glyph = 0;
     hb_set_t remaining;
     for (auto old_gid : all_gids_to_retain->iter ())
     {
+      if (old_gid == 0) {
+        reverse_glyph_map->set(0, 0);
+        continue;
+      }
+
       hb_codepoint_t* new_gid;
       if (!requested_glyph_map->has (old_gid, &new_gid))
       {
@@ -793,7 +799,7 @@ _create_old_gid_to_new_gid_map (const hb_face_t *face,
         continue;
       }
 
-      if (*new_gid > max_glyph || max_glyph == HB_SET_VALUE_INVALID)
+      if (*new_gid > max_glyph)
         max_glyph = *new_gid;
       reverse_glyph_map->set (*new_gid, old_gid);
     }
diff --git a/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto.41,43,61,66,69.ttf b/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto.41,43,61,66,69.ttf
new file mode 100644
index 000000000..a4c82662f
Binary files /dev/null and b/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto.41,43,61,66,69.ttf differ
diff --git a/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto_retain_gids.41,43,61,66,69.ttf b/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto_retain_gids.41,43,61,66,69.ttf
new file mode 100644
index 000000000..f63599984
Binary files /dev/null and b/test/subset/data/expected/glyph_map/Roboto-Regular.glyph_map_roboto_retain_gids.41,43,61,66,69.ttf differ
diff --git a/test/subset/data/profiles/glyph_map_roboto.txt b/test/subset/data/profiles/glyph_map_roboto.txt
new file mode 100644
index 000000000..2ee33b3cf
--- /dev/null
+++ b/test/subset/data/profiles/glyph_map_roboto.txt
@@ -0,0 +1,2 @@
+--gid-map=37:1,39:2,69:3,74:4,77:5
+--layout-features+=c2sc
diff --git a/test/subset/data/profiles/glyph_map_roboto_retain_gids.txt b/test/subset/data/profiles/glyph_map_roboto_retain_gids.txt
new file mode 100644
index 000000000..77a513cbb
--- /dev/null
+++ b/test/subset/data/profiles/glyph_map_roboto_retain_gids.txt
@@ -0,0 +1,4 @@
+--gid-map=37:37,39:39,69:69,74:74,77:77,444:444,446:446,561:561,563:563
+--gids=444,446,561,563
+--layout-features+=c2sc
+--retain-gids
diff --git a/test/subset/data/tests/glyph_map.tests b/test/subset/data/tests/glyph_map.tests
new file mode 100644
index 000000000..d222aceee
--- /dev/null
+++ b/test/subset/data/tests/glyph_map.tests
@@ -0,0 +1,9 @@
+FONTS:
+Roboto-Regular.ttf
+
+PROFILES:
+glyph_map_roboto.txt
+glyph_map_roboto_retain_gids.txt
+
+SUBSETS:
+ACafi
diff --git a/test/subset/generate-expected-outputs.py b/test/subset/generate-expected-outputs.py
index 201fe4a78..5f21f80c4 100755
--- a/test/subset/generate-expected-outputs.py
+++ b/test/subset/generate-expected-outputs.py
@@ -51,7 +51,9 @@ def generate_expected_output(input_file, unicodes, profile_flags, instance_flags
 	if unicodes != "":
 		args.extend(["--unicodes=%s" % unicodes,])
 
-	args.extend(profile_flags)
+	# --gid-map is unsupported in fonttools so don't send it. Tests using
+	# it are crafted to work without fonttools knowing about the flag.
+	args.extend([f for f in profile_flags if not f.startswith("--gid-map")])
 	if not no_fonttools:
 		check_call(args)