diff --git a/src/hb-ot-cff1-table.hh b/src/hb-ot-cff1-table.hh
index 089c2e0bb..b3bacd88e 100644
--- a/src/hb-ot-cff1-table.hh
+++ b/src/hb-ot-cff1-table.hh
@@ -28,6 +28,7 @@
 #define HB_OT_CFF1_TABLE_HH
 
 #include "hb-ot-cff-common.hh"
+#include "hb-subset-cff-common.hh"
 #include "hb-draw.hh"
 #include "hb-paint.hh"
 
@@ -1489,11 +1490,18 @@ struct cff1
   struct accelerator_subset_t : accelerator_templ_t<cff1_private_dict_opset_subset_t, cff1_private_dict_values_subset_t>
   {
     accelerator_subset_t (hb_face_t *face) : SUPER (face) {}
+    ~accelerator_subset_t ()
+    {
+      if (cff_accelerator)
+	cff_subset_accelerator_t::destroy (cff_accelerator);
+    }
 
     HB_INTERNAL bool subset (hb_subset_context_t *c) const;
     HB_INTERNAL bool serialize (hb_serialize_context_t *c,
 				struct cff1_subset_plan &plan) const;
 
+    mutable CFF::cff_subset_accelerator_t* cff_accelerator = nullptr;
+
     typedef accelerator_templ_t<cff1_private_dict_opset_subset_t, cff1_private_dict_values_subset_t> SUPER;
   };
 
diff --git a/src/hb-ot-cff2-table.hh b/src/hb-ot-cff2-table.hh
index a005de797..b62d182a0 100644
--- a/src/hb-ot-cff2-table.hh
+++ b/src/hb-ot-cff2-table.hh
@@ -28,6 +28,7 @@
 #define HB_OT_CFF2_TABLE_HH
 
 #include "hb-ot-cff-common.hh"
+#include "hb-subset-cff-common.hh"
 #include "hb-draw.hh"
 #include "hb-paint.hh"
 
@@ -520,12 +521,19 @@ struct cff2
   struct accelerator_subset_t : accelerator_templ_t<cff2_private_dict_opset_subset_t, cff2_private_dict_values_subset_t>
   {
     accelerator_subset_t (hb_face_t *face) : SUPER (face) {}
+    ~accelerator_subset_t ()
+    {
+      if (cff_accelerator)
+	cff_subset_accelerator_t::destroy (cff_accelerator);
+    }
 
     HB_INTERNAL bool subset (hb_subset_context_t *c) const;
     HB_INTERNAL bool serialize (hb_serialize_context_t *c,
 				struct cff2_subset_plan &plan,
 				hb_array_t<int> normalized_coords) const;
 
+    mutable CFF::cff_subset_accelerator_t* cff_accelerator = nullptr;
+
     typedef accelerator_templ_t<cff2_private_dict_opset_subset_t, cff2_private_dict_values_subset_t> SUPER;
   };
 
diff --git a/src/hb-subset-accelerator.hh b/src/hb-subset-accelerator.hh
index 1cdb57eb3..c7304c0aa 100644
--- a/src/hb-subset-accelerator.hh
+++ b/src/hb-subset-accelerator.hh
@@ -90,8 +90,6 @@ struct hb_subset_accelerator_t
     cmap_cache(nullptr),
     destroy_cmap_cache(nullptr),
     has_seac(has_seac_),
-    cff_accelerator(nullptr),
-    destroy_cff_accelerator(nullptr),
     source(hb_face_reference (source))
   {
     gid_to_unicodes.resize (unicode_to_gid.get_population ());
@@ -120,8 +118,6 @@ struct hb_subset_accelerator_t
 
   // CFF
   bool has_seac;
-  const CFF::cff_subset_accelerator_t* cff_accelerator;
-  hb_destroy_func_t destroy_cff_accelerator;
 
   // TODO(garretrieger): cumulative glyf checksum map
 
diff --git a/src/hb-subset-cff-common.hh b/src/hb-subset-cff-common.hh
index 9c0b2f422..3ef8dc2b0 100644
--- a/src/hb-subset-cff-common.hh
+++ b/src/hb-subset-cff-common.hh
@@ -678,8 +678,8 @@ struct subr_subsetter_t
   {
     unsigned fd_count = acc.fdCount;
     const cff_subset_accelerator_t* cff_accelerator = nullptr;
-    if (plan->accelerator && plan->accelerator->cff_accelerator) {
-      cff_accelerator = plan->accelerator->cff_accelerator;
+    if (acc.cff_accelerator) {
+      cff_accelerator = acc.cff_accelerator;
       fd_count = cff_accelerator->parsed_local_subrs.length;
     }
 
@@ -1126,14 +1126,11 @@ struct subr_subsetter_t
 
     compact_parsed_subrs ();
 
-    plan->inprogress_accelerator->cff_accelerator =
+    acc.cff_accelerator =
         cff_subset_accelerator_t::create(acc.blob,
                                          parsed_charstrings,
                                          parsed_global_subrs_storage,
                                          parsed_local_subrs_storage);
-    plan->inprogress_accelerator->destroy_cff_accelerator =
-        cff_subset_accelerator_t::destroy;
-
   }
 
   const parsed_cs_str_t& get_parsed_charstring (unsigned i) const
diff --git a/src/hb-subset-cff1.cc b/src/hb-subset-cff1.cc
index 9a48c900b..958609932 100644
--- a/src/hb-subset-cff1.cc
+++ b/src/hb-subset-cff1.cc
@@ -492,12 +492,11 @@ struct cff1_subset_plan
       return;
     }
 
-    hb_vector_t<uint16_t> *glyph_to_sid_map = (plan->accelerator && plan->accelerator->cff_accelerator) ?
-					       plan->accelerator->cff_accelerator->glyph_to_sid_map.get_acquire () :
-					       nullptr;
+    hb_vector_t<uint16_t> *glyph_to_sid_map = acc.cff_accelerator ?
+					      acc.cff_accelerator->glyph_to_sid_map.get_acquire () :
+					      nullptr;
     bool created_map = false;
-    if (!glyph_to_sid_map &&
-	((plan->accelerator && plan->accelerator->cff_accelerator)))
+    if (!glyph_to_sid_map && acc.cff_accelerator)
     {
       created_map = true;
       glyph_to_sid_map = acc.create_glyph_to_sid_map ();
@@ -541,8 +540,8 @@ struct cff1_subset_plan
 
     if (created_map)
     {
-      if (!(plan->accelerator && plan->accelerator->cff_accelerator) ||
-	  !plan->accelerator->cff_accelerator->glyph_to_sid_map.cmpexch (nullptr, glyph_to_sid_map))
+      if ((!plan->accelerator && acc.cff_accelerator) ||
+	  !acc.cff_accelerator->glyph_to_sid_map.cmpexch (nullptr, glyph_to_sid_map))
       {
 	glyph_to_sid_map->~hb_vector_t ();
 	hb_free (glyph_to_sid_map);
diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index 097d46f7b..36d6afef7 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -51,9 +51,6 @@ using OT::Layout::GPOS;
 
 hb_subset_accelerator_t::~hb_subset_accelerator_t ()
 {
-  if (cff_accelerator && destroy_cff_accelerator)
-    destroy_cff_accelerator ((void*) cff_accelerator);
-
   if (cmap_cache && destroy_cmap_cache)
     destroy_cmap_cache ((void*) cmap_cache);
 
diff --git a/src/hb-subset.cc b/src/hb-subset.cc
index cda78e1e4..996d1faf2 100644
--- a/src/hb-subset.cc
+++ b/src/hb-subset.cc
@@ -68,13 +68,17 @@ template<>
 struct hb_subset_plan_t::source_table_loader<const OT::cff1>
 {
   auto operator () (hb_subset_plan_t *plan)
-  HB_AUTO_RETURN (plan->accelerator ? plan->accelerator->cff1_accel : plan->cff1_accel)
+  HB_AUTO_RETURN (plan->accelerator ? plan->accelerator->cff1_accel :
+		  plan->inprogress_accelerator ? plan->inprogress_accelerator->cff1_accel :
+		  plan->cff1_accel)
 };
 template<>
 struct hb_subset_plan_t::source_table_loader<const OT::cff2>
 {
   auto operator () (hb_subset_plan_t *plan)
-  HB_AUTO_RETURN (plan->accelerator ? plan->accelerator->cff2_accel : plan->cff2_accel)
+  HB_AUTO_RETURN (plan->accelerator ? plan->accelerator->cff2_accel :
+		  plan->inprogress_accelerator ? plan->inprogress_accelerator->cff2_accel :
+		  plan->cff2_accel)
 };
 #endif