diff --git a/src/hb-ot-cff1-table.hh b/src/hb-ot-cff1-table.hh
index 7e8942934..b5047002a 100644
--- a/src/hb-ot-cff1-table.hh
+++ b/src/hb-ot-cff1-table.hh
@@ -327,6 +327,12 @@ struct Charset0 {
       return sids[glyph - 1];
   }
 
+  void collect_glyph_to_sid_map (hb_map_t *mapping, unsigned int num_glyphs) const
+  {
+    for (hb_codepoint_t gid = 1; gid < num_glyphs; gid++)
+      mapping->set (gid, sids[gid - 1]);
+  }
+
   hb_codepoint_t get_glyph (hb_codepoint_t sid, unsigned int num_glyphs) const
   {
     if (sid == 0)
@@ -390,13 +396,28 @@ struct Charset1_2 {
     for (unsigned int i = 0;; i++)
     {
       if (glyph <= ranges[i].nLeft)
-	return (hb_codepoint_t)ranges[i].first + glyph;
+	return (hb_codepoint_t) ranges[i].first + glyph;
       glyph -= (ranges[i].nLeft + 1);
     }
 
     return 0;
   }
 
+  void collect_glyph_to_sid_map (hb_map_t *mapping, unsigned int num_glyphs) const
+  {
+    hb_codepoint_t gid = 1;
+    for (unsigned i = 0;; i++)
+    {
+      hb_codepoint_t sid = ranges[i].first;
+      unsigned count = ranges[i].nLeft + 1;
+      for (unsigned j = 0; j < count; j++)
+	mapping->set (gid++, sid++);
+
+      if (gid >= num_glyphs)
+        break;
+    }
+  }
+
   hb_codepoint_t get_glyph (hb_codepoint_t sid, unsigned int num_glyphs) const
   {
     if (sid == 0) return 0;
@@ -532,6 +553,17 @@ struct Charset
     }
   }
 
+  void collect_glyph_to_sid_map (hb_map_t *mapping, unsigned int num_glyphs) const
+  {
+    switch (format)
+    {
+    case 0: u.format0.collect_glyph_to_sid_map (mapping, num_glyphs); return;
+    case 1: u.format1.collect_glyph_to_sid_map (mapping, num_glyphs); return;
+    case 2: u.format2.collect_glyph_to_sid_map (mapping, num_glyphs); return;
+    default:return;
+    }
+  }
+
   hb_codepoint_t get_glyph (hb_codepoint_t sid, unsigned int num_glyphs) const
   {
     switch (format)
@@ -1196,6 +1228,19 @@ struct cff1
       }
     }
 
+    hb_map_t *create_glyph_to_sid_map () const
+    {
+      if (charset != &Null (Charset))
+      {
+	hb_map_t *mapping = hb_map_create ();
+	mapping->set (0, 0);
+	charset->collect_glyph_to_sid_map (mapping, num_glyphs);
+	return mapping;
+      }
+      else
+	return nullptr;
+    }
+
     hb_codepoint_t glyph_to_sid (hb_codepoint_t glyph) const
     {
       if (charset != &Null (Charset))
diff --git a/src/hb-subset-cff1.cc b/src/hb-subset-cff1.cc
index 8a3034db0..52bb13d32 100644
--- a/src/hb-subset-cff1.cc
+++ b/src/hb-subset-cff1.cc
@@ -442,6 +442,9 @@ struct cff_subset_plan {
       return;
     }
 
+    bool use_glyph_to_sid_map = plan->num_output_glyphs () > plan->source->get_num_glyphs () / 8.;
+    hb_map_t *glyph_to_sid_map = use_glyph_to_sid_map ? acc.create_glyph_to_sid_map () : nullptr;
+
     unsigned int glyph;
     for (glyph = 1; glyph < plan->num_output_glyphs (); glyph++)
     {
@@ -451,7 +454,7 @@ struct cff_subset_plan {
 	/* Retain the SID for the old missing glyph ID */
 	old_glyph = glyph;
       }
-      sid = acc.glyph_to_sid (old_glyph);
+      sid = glyph_to_sid_map ? glyph_to_sid_map->get (old_glyph) : acc.glyph_to_sid (old_glyph);
 
       if (!acc.is_CID ())
 	sid = sidmap.add (sid);
@@ -464,6 +467,9 @@ struct cff_subset_plan {
       last_sid = sid;
     }
 
+    if (glyph_to_sid_map)
+      hb_map_destroy (glyph_to_sid_map);
+
     bool two_byte = subset_charset_ranges.complete (glyph);
 
     size0 = Charset0::min_size + HBUINT16::static_size * (plan->num_output_glyphs () - 1);