diff --git a/src/hb-subset-plan.cc b/src/hb-subset-plan.cc
index 84a3fbc5f..4d078b7e3 100644
--- a/src/hb-subset-plan.cc
+++ b/src/hb-subset-plan.cc
@@ -400,6 +400,13 @@ _nameid_closure (hb_face_t *face,
 #endif
 }
 
+static hb_set_t* copy (const hb_set_t* other)
+{
+  hb_set_t* set = hb_set_create ();
+  set->set (other);
+  return set;
+}
+
 /**
  * hb_subset_plan_create:
  * Computes a plan for subsetting the supplied face according
@@ -412,7 +419,7 @@ _nameid_closure (hb_face_t *face,
  **/
 hb_subset_plan_t *
 hb_subset_plan_create (hb_face_t         *face,
-		       hb_subset_input_t *input)
+		       const hb_subset_input_t *input)
 {
   hb_subset_plan_t *plan;
   if (unlikely (!(plan = hb_object_create<hb_subset_plan_t> ())))
@@ -428,12 +435,12 @@ hb_subset_plan_create (hb_face_t         *face,
   plan->prune_unicode_ranges = !input->no_prune_unicode_ranges;
   plan->retain_all_layout_features = input->retain_all_layout_features;
   plan->unicodes = hb_set_create ();
-  plan->name_ids = hb_set_reference (input->name_ids);
+  plan->name_ids = copy (plan->name_ids);
   _nameid_closure (face, plan->name_ids);
-  plan->name_languages = hb_set_reference (input->name_languages);
-  plan->layout_features = hb_set_reference (input->layout_features);
-  plan->glyphs_requested = hb_set_reference (input->glyphs);
-  plan->drop_tables = hb_set_reference (input->drop_tables);
+  plan->name_languages = copy (input->name_languages);
+  plan->layout_features = copy (input->layout_features);
+  plan->glyphs_requested = copy (input->glyphs);
+  plan->drop_tables = copy (input->drop_tables);
   plan->source = hb_face_reference (face);
   plan->dest = hb_face_builder_create ();
 
diff --git a/src/hb-subset-plan.hh b/src/hb-subset-plan.hh
index 01117f4b0..6f832ee42 100644
--- a/src/hb-subset-plan.hh
+++ b/src/hb-subset-plan.hh
@@ -204,7 +204,7 @@ typedef struct hb_subset_plan_t hb_subset_plan_t;
 
 HB_INTERNAL hb_subset_plan_t *
 hb_subset_plan_create (hb_face_t           *face,
-		       hb_subset_input_t   *input);
+		       const hb_subset_input_t   *input);
 
 HB_INTERNAL void
 hb_subset_plan_destroy (hb_subset_plan_t *plan);
diff --git a/src/hb-subset.cc b/src/hb-subset.cc
index d91699de4..1b8cc2967 100644
--- a/src/hb-subset.cc
+++ b/src/hb-subset.cc
@@ -303,7 +303,7 @@ _subset_table (hb_subset_plan_t *plan, hb_tag_t tag)
  * Subsets a font according to provided input.
  **/
 hb_face_t *
-hb_subset (hb_face_t *source, hb_subset_input_t *input)
+hb_subset (hb_face_t *source, const hb_subset_input_t *input)
 {
   if (unlikely (!input || !source)) return hb_face_get_empty ();
 
diff --git a/src/hb-subset.h b/src/hb-subset.h
index 249540f02..1df8cfbbf 100644
--- a/src/hb-subset.h
+++ b/src/hb-subset.h
@@ -119,7 +119,7 @@ hb_subset_input_get_no_prune_unicode_ranges (hb_subset_input_t *subset_input);
 
 /* hb_subset () */
 HB_EXTERN hb_face_t *
-hb_subset (hb_face_t *source, hb_subset_input_t *input);
+hb_subset (hb_face_t *source, const hb_subset_input_t *input);
 
 
 HB_END_DECLS