diff --git a/src/hb-open-type-private.hh b/src/hb-open-type-private.hh
index f6081f07af0ad9b36158152788aea45c59a1373e..0b17effa02d82c6cbb0b7b325e19708cb6d1e813 100644
--- a/src/hb-open-type-private.hh
+++ b/src/hb-open-type-private.hh
@@ -692,8 +692,8 @@ struct FixedVersion
  * Use: (base+offset)
  */
 
-template <typename Type, typename OffsetType=Offset>
-struct OffsetTo : OffsetType
+template <typename Type, typename OffsetType=USHORT>
+struct OffsetTo : GenericOffset<OffsetType>
 {
   inline const Type& operator () (const void *base) const
   {
@@ -737,16 +737,14 @@ static inline const Type& operator + (const Base &base, const OffsetTo<Type, Off
 template <typename Base, typename OffsetType, typename Type>
 static inline Type& operator + (Base &base, OffsetTo<Type, OffsetType> &offset) { return offset (base); }
 
-template <typename Type>
-struct LongOffsetTo : OffsetTo<Type, LongOffset> {};
-
 
 /*
  * Array Types
  */
 
-template <typename Type, typename LenType>
-struct GenericArrayOf
+/* An array with a number of elements. */
+template <typename Type, typename LenType=USHORT>
+struct ArrayOf
 {
   const Type *sub_array (unsigned int start_offset, unsigned int *pcount /* IN/OUT */) const
   {
@@ -852,13 +850,9 @@ struct GenericArrayOf
   DEFINE_SIZE_ARRAY (sizeof (LenType), array);
 };
 
-/* An array with a USHORT number of elements. */
-template <typename Type>
-struct ArrayOf : GenericArrayOf<Type, USHORT> {};
-
 /* An array with a ULONG number of elements. */
 template <typename Type>
-struct LongArrayOf : GenericArrayOf<Type, ULONG> {};
+struct LongArrayOf : ArrayOf<Type, ULONG> {};
 
 /* Array of Offset's */
 template <typename Type>
@@ -866,11 +860,11 @@ struct OffsetArrayOf : ArrayOf<OffsetTo<Type> > {};
 
 /* Array of LongOffset's */
 template <typename Type>
-struct LongOffsetArrayOf : ArrayOf<LongOffsetTo<Type> > {};
+struct LongOffsetArrayOf : ArrayOf<OffsetTo<Type, ULONG> > {};
 
 /* LongArray of LongOffset's */
 template <typename Type>
-struct LongOffsetLongArrayOf : LongArrayOf<LongOffsetTo<Type> > {};
+struct LongOffsetLongArrayOf : LongArrayOf<OffsetTo<Type, ULONG> > {};
 
 /* Array of offsets relative to the beginning of the array itself. */
 template <typename Type>
@@ -951,8 +945,8 @@ struct HeadlessArrayOf
 
 
 /* An array with sorted elements.  Supports binary searching. */
-template <typename Type, typename LenType>
-struct GenericSortedArrayOf : GenericArrayOf<Type, LenType>
+template <typename Type, typename LenType=USHORT>
+struct SortedArrayOf : ArrayOf<Type, LenType>
 {
   template <typename SearchType>
   inline int bsearch (const SearchType &x) const
@@ -974,13 +968,9 @@ struct GenericSortedArrayOf : GenericArrayOf<Type, LenType>
   }
 };
 
-/* A sorted array with a USHORT number of elements. */
-template <typename Type>
-struct SortedArrayOf : GenericSortedArrayOf<Type, USHORT> {};
-
 /* A sorted array with a ULONG number of elements. */
 template <typename Type>
-struct LongSortedArrayOf : GenericSortedArrayOf<Type, ULONG> {};
+struct LongSortedArrayOf : SortedArrayOf<Type, ULONG> {};
 
 
 } /* namespace OT */
diff --git a/src/hb-ot-cmap-table.hh b/src/hb-ot-cmap-table.hh
index a50dca68ef379ecd8b7286ad8cdc1a798e7323ed..abdd8db41f866db74e6b6ccb5d677ee74dc4e5f3 100644
--- a/src/hb-ot-cmap-table.hh
+++ b/src/hb-ot-cmap-table.hh
@@ -229,7 +229,7 @@ struct CmapSubtableTrimmed
   UINT		length;		/* Byte length of this subtable. */
   UINT		language;	/* Ignore. */
   UINT		startCharCode;	/* First character code covered. */
-  GenericArrayOf<GlyphID, UINT>
+  ArrayOf<GlyphID, UINT>
 		glyphIdArray;	/* Array of glyph index values for character
 				 * codes in the range. */
   public:
@@ -350,7 +350,7 @@ struct EncodingRecord
 
   USHORT	platformID;	/* Platform ID. */
   USHORT	encodingID;	/* Platform-specific encoding ID. */
-  LongOffsetTo<CmapSubtable>
+  OffsetTo<CmapSubtable, ULONG>
 		subtable;	/* Byte offset from beginning of table to the subtable for this encoding. */
   public:
   DEFINE_SIZE_STATIC (8);
diff --git a/src/hb-ot-layout-common-private.hh b/src/hb-ot-layout-common-private.hh
index 3904c2dd67899d9c5b5aa5d0ee78de0e1bd9a709..479fb26509145b91b23baf75fd8fed5b58e13529 100644
--- a/src/hb-ot-layout-common-private.hh
+++ b/src/hb-ot-layout-common-private.hh
@@ -506,7 +506,7 @@ struct Feature
     if (unlikely (!featureParams.sanitize (c, this, closure ? closure->tag : HB_TAG_NONE)))
       return TRACE_RETURN (false);
 
-    if (likely (!orig_offset))
+    if (likely (orig_offset.is_null ()))
       return TRACE_RETURN (true);
 
     if (featureParams == 0 && closure &&