diff --git a/src/hb-ot-glyf-table.hh b/src/hb-ot-glyf-table.hh
index b4ac68834..866bb7e04 100644
--- a/src/hb-ot-glyf-table.hh
+++ b/src/hb-ot-glyf-table.hh
@@ -953,6 +953,8 @@ struct glyf
       glyf_table.destroy ();
     }
 
+    bool has_data () const { return num_glyphs; }
+
     protected:
     template<typename T>
     bool get_points (hb_font_t *font, hb_codepoint_t gid, T consumer) const
diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index 0b11b6042..b84478611 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -393,16 +393,19 @@ _populate_gids_to_retain (hb_subset_plan_t* plan,
   _remove_invalid_gids (&cur_glyphset, plan->source->get_num_glyphs ());
 
   hb_set_set (plan->_glyphset_colred, &cur_glyphset);
-  // Populate a full set of glyphs to retain by adding all referenced
-  // composite glyphs.
-  for (hb_codepoint_t gid : cur_glyphset)
-  {
-    glyf.add_gid_and_children (gid, plan->_glyphset);
+
+  /* Populate a full set of glyphs to retain by adding all referenced
+   * composite glyphs. */
+  if (glyf.has_data ())
+    for (hb_codepoint_t gid : cur_glyphset)
+      glyf.add_gid_and_children (gid, plan->_glyphset);
+  else
+    plan->_glyphset->union_ (cur_glyphset);
 #ifndef HB_NO_SUBSET_CFF
-    if (cff.is_valid ())
+  if (cff.is_valid ())
+    for (hb_codepoint_t gid : cur_glyphset)
       _add_cff_seac_components (cff, gid, plan->_glyphset);
 #endif
-  }
 
   _remove_invalid_gids (plan->_glyphset, plan->source->get_num_glyphs ());