diff --git a/src/hb-ot-var-common.hh b/src/hb-ot-var-common.hh
index ae6a0bda8..9a33af299 100644
--- a/src/hb-ot-var-common.hh
+++ b/src/hb-ot-var-common.hh
@@ -251,7 +251,8 @@ struct TupleVariationHeader
 
   bool unpack_axis_tuples (unsigned axis_count,
                            const hb_array_t<const F2DOT14> shared_tuples,
-                           hb_hashmap_t<unsigned, Triple>& axis_tuples /* OUT */) const
+                           const hb_map_t *axes_old_index_tag_map,
+                           hb_hashmap_t<hb_tag_t, Triple>& axis_tuples /* OUT */) const
   {
     const F2DOT14 *peak_tuple = nullptr;
     if (has_peak ())
@@ -279,6 +280,10 @@ struct TupleVariationHeader
       float peak = peak_tuple[i].to_float ();
       if (peak == 0.f) continue;
 
+      hb_tag_t *axis_tag;
+      if (!axes_old_index_tag_map->has (i, &axis_tag))
+        return false;
+
       float start, end;
       if (has_interm)
       {
@@ -290,7 +295,7 @@ struct TupleVariationHeader
         start = hb_min (peak, 0.f);
         end = hb_max (peak, 0.f);
       }
-      axis_tuples.set (i, Triple (start, peak, end));
+      axis_tuples.set (*axis_tag, Triple (start, peak, end));
     }
 
     return true;
@@ -562,6 +567,7 @@ struct TupleVariationData
                                      unsigned tuple_var_count,
                                      unsigned point_count,
                                      bool is_gvar,
+                                     const hb_map_t *axes_old_index_tag_map,
                                      const hb_vector_t<unsigned> &shared_indices,
                                      const hb_array_t<const F2DOT14> shared_tuples)
     {
@@ -572,8 +578,8 @@ struct TupleVariationData
         if (unlikely (!iterator.var_data_bytes.check_range (p, length)))
         { fini (); return false; }
 
-        hb_hashmap_t<unsigned, Triple> axis_tuples;
-        if (!iterator.current_tuple->unpack_axis_tuples (iterator.get_axis_count (), shared_tuples, axis_tuples)
+        hb_hashmap_t<hb_tag_t, Triple> axis_tuples;
+        if (!iterator.current_tuple->unpack_axis_tuples (iterator.get_axis_count (), shared_tuples, axes_old_index_tag_map, axis_tuples)
             || axis_tuples.is_empty ())
         { fini (); return false; }
 
@@ -849,12 +855,14 @@ struct TupleVariationData
   bool decompile_tuple_variations (unsigned point_count,
                                    bool is_gvar,
                                    tuple_iterator_t iterator,
+                                   const hb_map_t *axes_old_index_tag_map,
                                    const hb_vector_t<unsigned> &shared_indices,
                                    const hb_array_t<const F2DOT14> shared_tuples,
                                    tuple_variations_t& tuple_variations /* OUT */) const
   {
     return tuple_variations.create_from_tuple_var_data (iterator, tupleVarCount,
                                                         point_count, is_gvar,
+                                                        axes_old_index_tag_map,
                                                         shared_indices,
                                                         shared_tuples);
   }
diff --git a/src/hb-ot-var-cvar-table.hh b/src/hb-ot-var-cvar-table.hh
index 110a3af40..c85da7adc 100644
--- a/src/hb-ot-var-cvar-table.hh
+++ b/src/hb-ot-var-cvar-table.hh
@@ -54,6 +54,7 @@ struct cvar
   bool decompile_tuple_variations (unsigned axis_count,
                                    unsigned point_count,
                                    bool is_gvar,
+                                   const hb_map_t *axes_old_index_tag_map,
                                    TupleVariationData::tuple_variations_t& tuple_variations /* OUT */) const
   {
     hb_vector_t<unsigned> shared_indices;
@@ -65,6 +66,7 @@ struct cvar
       return false;
 
     return tupleVariationData.decompile_tuple_variations (point_count, is_gvar, iterator,
+                                                          axes_old_index_tag_map,
                                                           shared_indices,
                                                           hb_array<const F2DOT14> (),
                                                           tuple_variations);
diff --git a/src/test-tuple-varstore.cc b/src/test-tuple-varstore.cc
index 569189677..8387d1e88 100644
--- a/src/test-tuple-varstore.cc
+++ b/src/test-tuple-varstore.cc
@@ -33,8 +33,13 @@ test_decompile_cvar ()
   const OT::cvar* cvar_table = reinterpret_cast<const OT::cvar*> (cvar_data);
   unsigned point_count = 65;
   unsigned axis_count = 1;
+
+  hb_tag_t axis_tag = HB_TAG ('w', 'g', 'h', 't');
+  hb_map_t axis_idx_tag_map;
+  axis_idx_tag_map.set (0, axis_tag);
+
   OT::TupleVariationData::tuple_variations_t tuple_variations;
-  bool result = cvar_table->decompile_tuple_variations (axis_count, point_count, false, tuple_variations);
+  bool result = cvar_table->decompile_tuple_variations (axis_count, point_count, false, &axis_idx_tag_map, tuple_variations);
   assert (result);
   assert (tuple_variations.tuple_vars.length == 2);
   for (unsigned i = 0; i < 2; i++)
@@ -44,8 +49,8 @@ test_decompile_cvar ()
     assert (tuple_variations.tuple_vars[i].indices.length == 65);
     assert (tuple_variations.tuple_vars[i].indices.length == tuple_variations.tuple_vars[i].deltas_x.length);
   }
-  assert (tuple_variations.tuple_vars[0].axis_tuples.get (0) == Triple (-1.f, -1.f, 0.f));
-  assert (tuple_variations.tuple_vars[1].axis_tuples.get (0) == Triple (0.f, 1.f, 1.f));
+  assert (tuple_variations.tuple_vars[0].axis_tuples.get (axis_tag) == Triple (-1.f, -1.f, 0.f));
+  assert (tuple_variations.tuple_vars[1].axis_tuples.get (axis_tag) == Triple (0.f, 1.f, 1.f));
   
   hb_vector_t<float> deltas_1 {0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, 0.f, -3.f, 1.f, 0.f, -1.f, 0.f, -3.f, 1.f, 0.f, -37.f, -37.f, -26.f, -26.f, 0.f, 0.f, 0.f, -3.f, 0.f, 0.f, 0.f, 0.f, 0.f, -3.f, 0.f, 2.f, -29.f, -29.f, -20.f, -20.f, 0.f, 0.f, 0.f, 1.f, -29.f, -29.f, -20.f, -20.f, 0.f, 0.f, 0.f, 1.f};
   for (unsigned i = 0; i < 65; i++)