diff --git a/src/hb-algs.hh b/src/hb-algs.hh
index e0700100b..ee604e88c 100644
--- a/src/hb-algs.hh
+++ b/src/hb-algs.hh
@@ -50,7 +50,7 @@ struct
 {
   private:
   template <typename T> auto
-  impl (const T& v, hb_priority<1>) const HB_RETURN (uint32_t, hb_deref_pointer (v).hash ())
+  impl (const T& v, hb_priority<1>) const HB_RETURN (uint32_t, hb_deref (v).hash ())
 
   template <typename T,
 	    hb_enable_if (hb_is_integer (T))> auto
@@ -73,17 +73,17 @@ struct
   /* Pointer-to-member-function. */
   template <typename Appl, typename Val1, typename ...Vals> auto
   impl (Appl&& a, hb_priority<2>, Val1 &&v1, Vals &&...vs) const HB_AUTO_RETURN
-  ((hb_deref_pointer (hb_forward<Val1> (v1)).*hb_forward<Appl> (a)) (hb_forward<Vals> (vs)...))
+  ((hb_deref (hb_forward<Val1> (v1)).*hb_forward<Appl> (a)) (hb_forward<Vals> (vs)...))
 
   /* Pointer-to-member. */
   template <typename Appl, typename Val> auto
   impl (Appl&& a, hb_priority<1>, Val &&v) const HB_AUTO_RETURN
-  ((hb_deref_pointer (hb_forward<Val> (v))).*hb_forward<Appl> (a))
+  ((hb_deref (hb_forward<Val> (v))).*hb_forward<Appl> (a))
 
   /* Operator(). */
   template <typename Appl, typename ...Vals> auto
   impl (Appl&& a, hb_priority<0>, Vals &&...vs) const HB_AUTO_RETURN
-  (hb_deref_pointer (hb_forward<Appl> (a)) (hb_forward<Vals> (vs)...))
+  (hb_deref (hb_forward<Appl> (a)) (hb_forward<Vals> (vs)...))
 
   public:
 
@@ -102,7 +102,7 @@ struct
 
   template <typename Pred, typename Val> auto
   impl (Pred&& p, Val &&v, hb_priority<1>) const HB_AUTO_RETURN
-  (hb_deref_pointer (hb_forward<Pred> (p)).has (v))
+  (hb_deref (hb_forward<Pred> (p)).has (v))
 
   template <typename Pred, typename Val> auto
   impl (Pred&& p, Val &&v, hb_priority<0>) const HB_AUTO_RETURN
@@ -127,7 +127,7 @@ struct
 
   template <typename Proj, typename Val> auto
   impl (Proj&& f, Val &&v, hb_priority<1>) const HB_AUTO_RETURN
-  (hb_deref_pointer (hb_forward<Proj> (f)).get (hb_forward<Val> (v)))
+  (hb_deref (hb_forward<Proj> (f)).get (hb_forward<Val> (v)))
 
   template <typename Proj, typename Val> auto
   impl (Proj&& f, Val &&v, hb_priority<0>) const HB_AUTO_RETURN
diff --git a/src/hb-map.hh b/src/hb-map.hh
index bbb1bef5d..f27ca9cae 100644
--- a/src/hb-map.hh
+++ b/src/hb-map.hh
@@ -57,7 +57,7 @@ struct hb_hashmap_t
 
     void clear () { key = kINVALID; value = vINVALID; }
 
-    bool operator == (K o) { return hb_deref_pointer (key) == hb_deref_pointer (o); }
+    bool operator == (K o) { return hb_deref (key) == hb_deref (o); }
     bool operator == (const item_t &o) { return *this == o.key; }
     bool is_unused () const    { return key == kINVALID; }
     bool is_tombstone () const { return key != kINVALID && value == vINVALID; }
diff --git a/src/hb-meta.hh b/src/hb-meta.hh
index b80358c2a..f7699d781 100644
--- a/src/hb-meta.hh
+++ b/src/hb-meta.hh
@@ -126,7 +126,7 @@ struct
   template <typename T> auto
   operator () (T *v) const HB_AUTO_RETURN (*v)
 
-} HB_FUNCOBJ (hb_deref_pointer);
+} HB_FUNCOBJ (hb_deref);
 
 
 template<bool B, typename T = void> struct hb_enable_if {};
diff --git a/src/hb-serialize.hh b/src/hb-serialize.hh
index d18934c4d..afaa4c4f9 100644
--- a/src/hb-serialize.hh
+++ b/src/hb-serialize.hh
@@ -132,7 +132,7 @@ struct hb_serialize_context_t
   { return check_equal (v1 = v2, v2); }
 
   template <typename T> bool propagate_error (T &&obj)
-  { return check_success (!hb_deref_pointer (obj).in_error ()); }
+  { return check_success (!hb_deref (obj).in_error ()); }
 
   template <typename T1, typename... Ts> bool propagate_error (T1 &&o1, Ts &&...os)
   { return propagate_error (hb_forward<T1> (o1)) &&