diff --git a/src/hb-open-type-private.hh b/src/hb-open-type-private.hh
index 0b17effa0..84e4aa23e 100644
--- a/src/hb-open-type-private.hh
+++ b/src/hb-open-type-private.hh
@@ -630,18 +630,15 @@ struct Index : USHORT {
 };
 DEFINE_NULL_DATA (Index, "\xff\xff");
 
-/* GenericOffset, Null offset = 0 */
-template <typename Type>
-struct GenericOffset : Type
+/* Offset, Null offset = 0 */
+template <typename Type=USHORT>
+struct Offset : Type
 {
   inline bool is_null (void) const { return 0 == *this; }
   public:
   DEFINE_SIZE_STATIC (sizeof(Type));
 };
 
-typedef GenericOffset<USHORT> Offset;
-typedef GenericOffset<ULONG>  LongOffset;
-
 
 /* CheckSum */
 struct CheckSum : ULONG
@@ -688,12 +685,12 @@ struct FixedVersion
 
 
 /*
- * Template subclasses of Offset and LongOffset that do the dereferencing.
+ * Template subclasses of Offset that do the dereferencing.
  * Use: (base+offset)
  */
 
 template <typename Type, typename OffsetType=USHORT>
-struct OffsetTo : GenericOffset<OffsetType>
+struct OffsetTo : Offset<OffsetType>
 {
   inline const Type& operator () (const void *base) const
   {
diff --git a/src/hb-ot-layout-common-private.hh b/src/hb-ot-layout-common-private.hh
index 479fb2650..2ed14a237 100644
--- a/src/hb-ot-layout-common-private.hh
+++ b/src/hb-ot-layout-common-private.hh
@@ -204,7 +204,7 @@ struct LangSys
     return TRACE_RETURN (c->check_struct (this) && featureIndex.sanitize (c));
   }
 
-  Offset	lookupOrder;	/* = Null (reserved for an offset to a
+  Offset<>	lookupOrder;	/* = Null (reserved for an offset to a
 				 * reordering table) */
   USHORT	reqFeatureIndex;/* Index of a feature required for this
 				 * language system--if no required features
@@ -502,7 +502,7 @@ struct Feature
      * Adobe tools, only the 'size' feature had FeatureParams defined.
      */
 
-    Offset orig_offset = featureParams;
+    Offset<> orig_offset = featureParams;
     if (unlikely (!featureParams.sanitize (c, this, closure ? closure->tag : HB_TAG_NONE)))
       return TRACE_RETURN (false);
 
@@ -516,7 +516,7 @@ struct Feature
       unsigned int new_offset_int = (unsigned int) orig_offset -
 				    (((char *) this) - ((char *) closure->list_base));
 
-      Offset new_offset;
+      Offset<> new_offset;
       /* Check that it did not overflow. */
       new_offset.set (new_offset_int);
       if (new_offset == new_offset_int &&
@@ -609,7 +609,7 @@ struct Lookup
 
   USHORT	lookupType;		/* Different enumerations for GSUB and GPOS */
   USHORT	lookupFlag;		/* Lookup qualifiers */
-  ArrayOf<Offset>
+  ArrayOf<Offset<> >
 		subTable;		/* Array of SubTables */
   USHORT	markFilteringSetX[VAR];	/* Index (base 0) into GDEF mark glyph sets
 					 * structure. This field is only present if bit