diff --git a/src/OT/glyf/CompositeGlyph.hh b/src/OT/glyf/CompositeGlyph.hh
index f0ff8e3e8..abe4c8330 100644
--- a/src/OT/glyf/CompositeGlyph.hh
+++ b/src/OT/glyf/CompositeGlyph.hh
@@ -25,13 +25,16 @@ struct CompositeGlyphRecord
     USE_MY_METRICS		= 0x0200,
     OVERLAP_COMPOUND		= 0x0400,
     SCALED_COMPONENT_OFFSET	= 0x0800,
-    UNSCALED_COMPONENT_OFFSET	= 0x1000
+    UNSCALED_COMPONENT_OFFSET	= 0x1000,
+    GID_IS_24BIT		= 0x2000
   };
 
   public:
   unsigned int get_size () const
   {
     unsigned int size = min_size;
+    /* glyphIndex is 24bit instead of 16bit */
+    if (flags & GID_IS_24BIT) size += HBGlyphID24::static_size - HBGlyphID16::static_size;
     /* arg1 and 2 are int16 */
     if (flags & ARG_1_AND_2_ARE_WORDS) size += 4;
     /* arg1 and 2 are int8 */
@@ -60,7 +63,11 @@ struct CompositeGlyphRecord
   bool is_anchored ()       const { return !(flags & ARGS_ARE_XY_VALUES); }
   void get_anchor_points (unsigned int &point1, unsigned int &point2) const
   {
-    const HBUINT8 *p = &StructAfter<const HBUINT8> (glyphIndex);
+    const auto *p = &StructAfter<const HBUINT8> (flags);
+    if (flags & GID_IS_24BIT)
+      p += HBGlyphID24::static_size;
+    else
+      p += HBGlyphID16::static_size;
     if (flags & ARG_1_AND_2_ARE_WORDS)
     {
       point1 = ((const HBUINT16 *) p)[0];
@@ -101,8 +108,12 @@ struct CompositeGlyphRecord
     matrix[0] = matrix[3] = 1.f;
     matrix[1] = matrix[2] = 0.f;
 
+    const auto *p = &StructAfter<const HBINT8> (flags);
+    if (flags & GID_IS_24BIT)
+      p += HBGlyphID24::static_size;
+    else
+      p += HBGlyphID16::static_size;
     int tx, ty;
-    const HBINT8 *p = &StructAfter<const HBINT8> (glyphIndex);
     if (flags & ARG_1_AND_2_ARE_WORDS)
     {
       tx = *(const HBINT16 *) p;
@@ -145,12 +156,25 @@ struct CompositeGlyphRecord
   }
 
   public:
-  hb_codepoint_t get_gid () const { return glyphIndex; }
-  void set_gid (hb_codepoint_t gid) { glyphIndex = gid; }
+  hb_codepoint_t get_gid () const
+  {
+    if (flags & GID_IS_24BIT)
+      return StructAfter<const HBGlyphID24> (flags);
+    else
+      return StructAfter<const HBGlyphID16> (flags);
+  }
+  void set_gid (hb_codepoint_t gid)
+  {
+    if (flags & GID_IS_24BIT)
+      StructAfter<HBGlyphID24> (flags) = gid;
+    else
+      /* TODO assert? */
+      StructAfter<HBGlyphID16> (flags) = gid;
+  }
 
   protected:
   HBUINT16	flags;
-  HBGlyphID16	glyphIndex;
+  HBUINT24	pad;
   public:
   DEFINE_SIZE_MIN (4);
 };