diff --git a/src/hb-open-type-private.hh b/src/hb-open-type-private.hh
index 6ad3c0fde..2f4e1b9e9 100644
--- a/src/hb-open-type-private.hh
+++ b/src/hb-open-type-private.hh
@@ -705,7 +705,7 @@ struct Index : UINT16 {
 DEFINE_NULL_DATA (Index, "\xff\xff");
 
 /* Offset, Null offset = 0 */
-template <typename Type=UINT16>
+template <typename Type>
 struct Offset : Type
 {
   inline bool is_null (void) const { return 0 == *this; }
@@ -713,6 +713,9 @@ struct Offset : Type
   DEFINE_SIZE_STATIC (sizeof(Type));
 };
 
+typedef Offset<UINT16> Offset16;
+typedef Offset<UINT32> Offset32;
+
 
 /* CheckSum */
 struct CheckSum : UINT32
diff --git a/src/hb-ot-layout-common-private.hh b/src/hb-ot-layout-common-private.hh
index dfbcf1efa..86a74ccb6 100644
--- a/src/hb-ot-layout-common-private.hh
+++ b/src/hb-ot-layout-common-private.hh
@@ -216,7 +216,7 @@ struct LangSys
     return_trace (c->check_struct (this) && featureIndex.sanitize (c));
   }
 
-  Offset<>	lookupOrderZ;	/* = Null (reserved for an offset to a
+  Offset16	lookupOrderZ;	/* = Null (reserved for an offset to a
 				 * reordering table) */
   UINT16	reqFeatureIndex;/* Index of a feature required for this
 				 * language system--if no required features
@@ -662,7 +662,7 @@ struct Lookup
   private:
   UINT16	lookupType;		/* Different enumerations for GSUB and GPOS */
   UINT16	lookupFlag;		/* Lookup qualifiers */
-  ArrayOf<Offset<> >
+  ArrayOf<Offset16>
 		subTable;		/* Array of SubTables */
   UINT16	markFilteringSetX[VAR];	/* Index (base 0) into GDEF mark glyph sets
 					 * structure. This field is only present if bit
diff --git a/src/hb-ot-name-table.hh b/src/hb-ot-name-table.hh
index e90e46c14..4c5b3c0f9 100644
--- a/src/hb-ot-name-table.hh
+++ b/src/hb-ot-name-table.hh
@@ -125,7 +125,7 @@ struct name
   /* We only implement format 0 for now. */
   UINT16	format;			/* Format selector (=0/1). */
   UINT16	count;			/* Number of name records. */
-  Offset<>	stringOffset;		/* Offset to start of string storage (from start of table). */
+  Offset16	stringOffset;		/* Offset to start of string storage (from start of table). */
   NameRecord	nameRecord[VAR];	/* The name records where count is the number of records. */
   public:
   DEFINE_SIZE_ARRAY (6, nameRecord);
diff --git a/src/hb-ot-var-fvar-table.hh b/src/hb-ot-var-fvar-table.hh
index ab7d35b43..2a9357a5e 100644
--- a/src/hb-ot-var-fvar-table.hh
+++ b/src/hb-ot-var-fvar-table.hh
@@ -186,7 +186,7 @@ struct fvar
   protected:
   FixedVersion<>version;	/* Version of the fvar table
 				 * initially set to 0x00010000u */
-  Offset<>	things;		/* Offset in bytes from the beginning of the table
+  Offset16	things;		/* Offset in bytes from the beginning of the table
 				 * to the start of the AxisRecord array. */
   UINT16	reserved;	/* This field is permanently reserved. Set to 2. */
   UINT16	axisCount;	/* The number of variation axes in the font (the