diff --git a/src/hb-array.hh b/src/hb-array.hh
index 2e7a4fa21..96d2e0a97 100644
--- a/src/hb-array.hh
+++ b/src/hb-array.hh
@@ -50,7 +50,7 @@ struct hb_array_t : hb_iter_with_fallback_t<hb_array_t<Type>, Type&>
   template <typename U,
 	    hb_enable_if (hb_is_cr_convertible(U, Type))>
   hb_array_t (const hb_array_t<U> &o) :
-    hb_iter_with_fallback_t<hb_array_t<Type>, Type&> (),
+    hb_iter_with_fallback_t<hb_array_t, Type&> (),
     arrayZ (o.arrayZ), length (o.length), backwards_length (o.backwards_length) {}
   template <typename U,
 	    hb_enable_if (hb_is_cr_convertible(U, Type))>
@@ -106,7 +106,7 @@ struct hb_array_t : hb_iter_with_fallback_t<hb_array_t<Type>, Type&>
    */
 
   /* Note: our compare is NOT lexicographic; it also does NOT call Type::cmp. */
-  int cmp (const hb_array_t<Type> &a) const
+  int cmp (const hb_array_t &a) const
   {
     if (length != a.length)
       return (int) a.length - (int) length;
@@ -114,8 +114,8 @@ struct hb_array_t : hb_iter_with_fallback_t<hb_array_t<Type>, Type&>
   }
   HB_INTERNAL static int cmp (const void *pa, const void *pb)
   {
-    hb_array_t<Type> *a = (hb_array_t<Type> *) pa;
-    hb_array_t<Type> *b = (hb_array_t<Type> *) pb;
+    hb_array_t *a = (hb_array_t *) pa;
+    hb_array_t *b = (hb_array_t *) pb;
     return b->cmp (*a);
   }
 
@@ -164,7 +164,7 @@ struct hb_array_t : hb_iter_with_fallback_t<hb_array_t<Type>, Type&>
 
   unsigned int get_size () const { return length * this->item_size; }
 
-  hb_array_t<Type> sub_array (unsigned int start_offset = 0, unsigned int *seg_count = nullptr /* IN/OUT */) const
+  hb_array_t sub_array (unsigned int start_offset = 0, unsigned int *seg_count = nullptr /* IN/OUT */) const
   {
     if (!start_offset && !seg_count)
       return *this;
@@ -176,9 +176,9 @@ struct hb_array_t : hb_iter_with_fallback_t<hb_array_t<Type>, Type&>
       count -= start_offset;
     if (seg_count)
       count = *seg_count = hb_min (count, *seg_count);
-    return hb_array_t<Type> (arrayZ + start_offset, count);
+    return hb_array_t (arrayZ + start_offset, count);
   }
-  hb_array_t<Type> sub_array (unsigned int start_offset, unsigned int seg_count) const
+  hb_array_t sub_array (unsigned int start_offset, unsigned int seg_count) const
   { return sub_array (start_offset, &seg_count); }
 
   template <typename T,
@@ -234,7 +234,7 @@ struct hb_sorted_array_t :
 	hb_iter_t<hb_sorted_array_t<Type>, Type&>,
 	hb_array_t<Type>
 {
-  typedef hb_iter_t<hb_sorted_array_t<Type>, Type&> iter_base_t;
+  typedef hb_iter_t<hb_sorted_array_t, Type&> iter_base_t;
   HB_ITER_USING (iter_base_t);
   static constexpr bool is_random_access_iterator = true;
   static constexpr bool is_sorted_iterator = true;
@@ -247,7 +247,7 @@ struct hb_sorted_array_t :
   template <typename U,
 	    hb_enable_if (hb_is_cr_convertible(U, Type))>
   hb_sorted_array_t (const hb_array_t<U> &o) :
-    hb_iter_t<hb_sorted_array_t<Type>, Type&> (),
+    hb_iter_t<hb_sorted_array_t, Type&> (),
     hb_array_t<Type> (o) {}
   template <typename U,
 	    hb_enable_if (hb_is_cr_convertible(U, Type))>
@@ -258,9 +258,9 @@ struct hb_sorted_array_t :
   bool operator != (const hb_sorted_array_t& o) const
   { return this->arrayZ != o.arrayZ || this->length != o.length; }
 
-  hb_sorted_array_t<Type> sub_array (unsigned int start_offset, unsigned int *seg_count /* IN/OUT */) const
-  { return hb_sorted_array_t<Type> (((const hb_array_t<Type> *) (this))->sub_array (start_offset, seg_count)); }
-  hb_sorted_array_t<Type> sub_array (unsigned int start_offset, unsigned int seg_count) const
+  hb_sorted_array_t sub_array (unsigned int start_offset, unsigned int *seg_count /* IN/OUT */) const
+  { return hb_sorted_array_t (((const hb_array_t<Type> *) (this))->sub_array (start_offset, seg_count)); }
+  hb_sorted_array_t sub_array (unsigned int start_offset, unsigned int seg_count) const
   { return sub_array (start_offset, &seg_count); }
 
   template <typename T>