diff --git a/src/hb-aat-layout-common.hh b/src/hb-aat-layout-common.hh
index 202cb2019..85332b0f7 100644
--- a/src/hb-aat-layout-common.hh
+++ b/src/hb-aat-layout-common.hh
@@ -164,7 +164,7 @@ struct LookupSegmentArray
 
   GlyphID	last;		/* Last GlyphID in this segment */
   GlyphID	first;		/* First GlyphID in this segment */
-  OffsetTo<UnsizedArrayOf<T>, HBUINT16, false>
+  NNOffsetTo<UnsizedArrayOf<T> >
 		valuesZ;	/* A 16-bit offset from the start of
 				 * the table to the data. */
   public:
@@ -629,11 +629,11 @@ struct StateTable
   protected:
   HBUINT	nClasses;	/* Number of classes, which is the number of indices
 				 * in a single line in the state array. */
-  OffsetTo<ClassType, HBUINT, false>
+  NNOffsetTo<ClassType, HBUINT>
 		classTable;	/* Offset to the class table. */
-  OffsetTo<UnsizedArrayOf<HBUSHORT>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<HBUSHORT>, HBUINT>
 		stateArrayTable;/* Offset to the state array. */
-  OffsetTo<UnsizedArrayOf<Entry<Extra> >, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<Entry<Extra> >, HBUINT>
 		entryTable;	/* Offset to the entry array. */
 
   public:
diff --git a/src/hb-aat-layout-kerx-table.hh b/src/hb-aat-layout-kerx-table.hh
index f52593926..b86c5131b 100644
--- a/src/hb-aat-layout-kerx-table.hh
+++ b/src/hb-aat-layout-kerx-table.hh
@@ -374,7 +374,7 @@ struct KerxSubTableFormat1
   protected:
   KernSubTableHeader				header;
   StateTable<Types, EntryData>			machine;
-  OffsetTo<UnsizedArrayOf<FWORD>, HBUINT, false>kernAction;
+  NNOffsetTo<UnsizedArrayOf<FWORD>, HBUINT>	kernAction;
   public:
   DEFINE_SIZE_STATIC (KernSubTableHeader::static_size + 5 * sizeof (HBUINT));
 };
@@ -443,13 +443,13 @@ struct KerxSubTableFormat2
   protected:
   KernSubTableHeader	header;
   HBUINT		rowWidth;	/* The width, in bytes, of a row in the table. */
-  OffsetTo<typename Types::ClassTypeWide, HBUINT, false>
+  NNOffsetTo<typename Types::ClassTypeWide, HBUINT>
 			leftClassTable;	/* Offset from beginning of this subtable to
 					 * left-hand class table. */
-  OffsetTo<typename Types::ClassTypeWide, HBUINT, false>
+  NNOffsetTo<typename Types::ClassTypeWide, HBUINT>
 			rightClassTable;/* Offset from beginning of this subtable to
 					 * right-hand class table. */
-  OffsetTo<UnsizedArrayOf<FWORD>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<FWORD>, HBUINT>
 			 array;		/* Offset from beginning of this subtable to
 					 * the start of the kerning array. */
   public:
@@ -719,18 +719,18 @@ struct KerxSubTableFormat6
   {
     struct Long
     {
-      LOffsetTo<Lookup<HBUINT32>, false>	rowIndexTable;
-      LOffsetTo<Lookup<HBUINT32>, false>	columnIndexTable;
-      LOffsetTo<UnsizedArrayOf<FWORD32>, false>	array;
+      LNNOffsetTo<Lookup<HBUINT32> >		rowIndexTable;
+      LNNOffsetTo<Lookup<HBUINT32> >		columnIndexTable;
+      LNNOffsetTo<UnsizedArrayOf<FWORD32> >	array;
     } l;
     struct Short
     {
-      LOffsetTo<Lookup<HBUINT16>, false>	rowIndexTable;
-      LOffsetTo<Lookup<HBUINT16>, false>	columnIndexTable;
-      LOffsetTo<UnsizedArrayOf<FWORD>, false>	array;
+      LNNOffsetTo<Lookup<HBUINT16> >		rowIndexTable;
+      LNNOffsetTo<Lookup<HBUINT16> >		columnIndexTable;
+      LNNOffsetTo<UnsizedArrayOf<FWORD> >	array;
     } s;
   } u;
-  LOffsetTo<UnsizedArrayOf<FWORD>, false>	vector;
+  LNNOffsetTo<UnsizedArrayOf<FWORD> >	vector;
   public:
   DEFINE_SIZE_STATIC (KernSubTableHeader::static_size + 24);
 };
diff --git a/src/hb-aat-layout-morx-table.hh b/src/hb-aat-layout-morx-table.hh
index 15686b657..d8a90bbd8 100644
--- a/src/hb-aat-layout-morx-table.hh
+++ b/src/hb-aat-layout-morx-table.hh
@@ -352,7 +352,7 @@ struct ContextualSubtable
   protected:
   StateTable<Types, EntryData>
 		machine;
-  OffsetTo<UnsizedOffsetListOf<Lookup<GlyphID>, HBUINT, false>, HBUINT, false>
+  NNOffsetTo<UnsizedOffsetListOf<Lookup<GlyphID>, HBUINT, false>, HBUINT>
 		substitutionTables;
   public:
   DEFINE_SIZE_STATIC (20);
@@ -591,11 +591,11 @@ struct LigatureSubtable
   protected:
   StateTable<Types, EntryData>
 		machine;
-  OffsetTo<UnsizedArrayOf<HBUINT32>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<HBUINT32>, HBUINT>
 		ligAction;	/* Offset to the ligature action table. */
-  OffsetTo<UnsizedArrayOf<HBUINT16>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<HBUINT16>, HBUINT>
 		component;	/* Offset to the component table. */
-  OffsetTo<UnsizedArrayOf<GlyphID>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<GlyphID>, HBUINT>
 		ligature;	/* Offset to the actual ligature lists. */
   public:
   DEFINE_SIZE_STATIC (28);
@@ -833,7 +833,7 @@ struct InsertionSubtable
   protected:
   StateTable<Types, EntryData>
 		machine;
-  OffsetTo<UnsizedArrayOf<GlyphID>, HBUINT, false>
+  NNOffsetTo<UnsizedArrayOf<GlyphID>, HBUINT>
 		insertionAction;	/* Byte offset from stateHeader to the start of
 					 * the insertion glyph table. */
   public: