diff --git a/src/OT/Color/CPAL/CPAL.hh b/src/OT/Color/CPAL/CPAL.hh
index 6646b083e..c07716c1c 100644
--- a/src/OT/Color/CPAL/CPAL.hh
+++ b/src/OT/Color/CPAL/CPAL.hh
@@ -73,6 +73,30 @@ struct CPALV1Tail
   }
 
   public:
+  void collect_name_ids (const void *base,
+                         unsigned palette_count,
+                         unsigned color_count,
+                         const hb_map_t *color_index_map,
+                         hb_set_t *nameids_to_retain /* OUT */) const
+  {
+    if (paletteLabelsZ)
+    {
+      + (base+paletteLabelsZ).as_array (palette_count)
+      | hb_sink (nameids_to_retain)
+      ;
+    }
+
+    if (colorLabelsZ)
+    {
+      const hb_array_t<const NameID> colorLabels = (base+colorLabelsZ).as_array (color_count);
+      for (unsigned i = 0; i < color_count; i++)
+      {
+        if (!color_index_map->has (i)) continue;
+        nameids_to_retain->add (colorLabels[i]);
+      }
+    }
+  }
+
   bool serialize (hb_serialize_context_t *c,
                   unsigned palette_count,
                   unsigned color_count,
@@ -186,6 +210,13 @@ struct CPAL
     return numColors;
   }
 
+  void collect_name_ids (const hb_map_t *color_index_map,
+                         hb_set_t *nameids_to_retain /* OUT */) const
+  {
+    if (version == 1)
+      v1 ().collect_name_ids (this, numPalettes, numColors, color_index_map, nameids_to_retain);
+  }
+
   private:
   const CPALV1Tail& v1 () const
   {
diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index 088fdca07..bf6fe1784 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -38,6 +38,7 @@
 #include "hb-ot-cff1-table.hh"
 #include "OT/Color/COLR/COLR.hh"
 #include "OT/Color/COLR/colrv1-closure.hh"
+#include "OT/Color/CPAL/CPAL.hh"
 #include "hb-ot-var-fvar-table.hh"
 #include "hb-ot-var-avar-table.hh"
 #include "hb-ot-stat-table.hh"
@@ -620,6 +621,26 @@ _glyf_add_gid_and_children (const OT::glyf_accelerator_t &glyf,
   return operation_count;
 }
 
+static void
+_nameid_closure (hb_face_t *face,
+		 hb_set_t  *nameids,
+		 bool all_axes_pinned,
+		 hb_hashmap_t<hb_tag_t, float> *user_axes_location,
+		 bool collect_cpal_name_ids,
+		 const hb_map_t *color_index_map)
+{
+#ifndef HB_NO_STYLE
+  face->table.STAT->collect_name_ids (user_axes_location, nameids);
+#endif
+#ifndef HB_NO_VAR
+  if (!all_axes_pinned)
+    face->table.fvar->collect_name_ids (user_axes_location, nameids);
+#endif
+
+  if (collect_cpal_name_ids)
+    face->table.CPAL->collect_name_ids (color_index_map, nameids);
+}
+
 static void
 _populate_gids_to_retain (hb_subset_plan_t* plan,
 		          hb_set_t* drop_tables)
@@ -673,6 +694,10 @@ _populate_gids_to_retain (hb_subset_plan_t* plan,
 
   plan->_glyphset_colred = cur_glyphset;
 
+  _nameid_closure (plan->source, &(plan->name_ids),
+                   plan->all_axes_pinned, &(plan->user_axes_location),
+                   !drop_tables->has (HB_OT_TAG_CPAL),
+                   &(plan->colr_palettes));
   /* Populate a full set of glyphs to retain by adding all referenced
    * composite glyphs. */
   if (glyf.has_data ())
@@ -756,21 +781,6 @@ _create_old_gid_to_new_gid_map (const hb_face_t *face,
   ;
 }
 
-static void
-_nameid_closure (hb_face_t *face,
-		 hb_set_t  *nameids,
-		 bool all_axes_pinned,
-		 hb_hashmap_t<hb_tag_t, float> *user_axes_location)
-{
-#ifndef HB_NO_STYLE
-  face->table.STAT->collect_name_ids (user_axes_location, nameids);
-#endif
-#ifndef HB_NO_VAR
-  if (!all_axes_pinned)
-    face->table.fvar->collect_name_ids (user_axes_location, nameids);
-#endif
-}
-
 #ifndef HB_NO_VAR
 static void
 _normalize_axes_location (hb_face_t *face, hb_subset_plan_t *plan)
@@ -905,7 +915,6 @@ hb_subset_plan_t::hb_subset_plan_t (hb_face_t *face,
         glyph_map->get(unicode_to_new_gid_list.arrayZ[i].second);
   }
 
-  _nameid_closure (face, &name_ids, all_axes_pinned, &user_axes_location);
   if (unlikely (in_error ()))
     return;