diff --git a/src/hb-ot-cff1-table.hh b/src/hb-ot-cff1-table.hh
index df6f61979..3471ee010 100644
--- a/src/hb-ot-cff1-table.hh
+++ b/src/hb-ot-cff1-table.hh
@@ -636,7 +636,7 @@ struct Charset
 struct CFF1StringIndex : CFF1Index
 {
   bool serialize (hb_serialize_context_t *c, const CFF1StringIndex &strings,
-		  const hb_inc_bimap_t &sidmap)
+		  const hb_map_t &sidmap)
   {
     TRACE_SERIALIZE (this);
     if (unlikely ((strings.count == 0) || (sidmap.get_population () == 0)))
diff --git a/src/hb-subset-cff1.cc b/src/hb-subset-cff1.cc
index 855c8c51a..308bb5944 100644
--- a/src/hb-subset-cff1.cc
+++ b/src/hb-subset-cff1.cc
@@ -39,12 +39,20 @@
 
 using namespace CFF;
 
-struct remap_sid_t : hb_inc_bimap_t
+struct remap_sid_t : hb_map_t
 {
   unsigned int add (unsigned int sid)
   {
     if ((sid != CFF_UNDEF_SID) && !is_std_std (sid))
-      return offset_sid (hb_inc_bimap_t::add (unoffset_sid (sid)));
+    {
+      sid = unoffset_sid (sid);
+      unsigned v = get (sid);
+      if (v != HB_MAP_VALUE_INVALID)
+        return offset_sid (v);
+      v = next++;
+      set (sid, v);
+      return offset_sid (v);
+    }
     else
       return sid;
   }
@@ -62,6 +70,7 @@ struct remap_sid_t : hb_inc_bimap_t
   static bool is_std_std (unsigned int sid) { return sid < num_std_strings; }
   static unsigned int offset_sid (unsigned int sid) { return sid + num_std_strings; }
   static unsigned int unoffset_sid (unsigned int sid) { return sid - num_std_strings; }
+  unsigned next = 0;
 };
 
 struct cff1_sub_table_info_t : cff_sub_table_info_t