diff --git a/ChangeLog b/ChangeLog
index 8cf5015be..e5bbe83fc 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,30 @@
+2016-07-08  Alexei Podtelezhnikov  <apodtele@gmail.com>
+
+	[smooth] Sub-banding protocol revision.
+
+	Rasterization sub-banding is utilized at large sizes while using
+	rather small fixed memory pool. Indeed it is possible to make an
+	educated guess how much memory is necessary at a given size for a
+	given glyph. It turns out that, for large majority of European glyphs,
+	you should store about 8 times more boundary pixels than their height.
+	Or, vice versa, if your memory pool can hold 800 pixels the band
+	height should be 100 and you should sub-band anything larger than
+	that. Should you still run out of memory, FreeType bisects the band
+	but you have wasted some time. This is what has been implemented in
+	FreeType since the beginning.
+
+	It was overlooked, however, that the top band could grow to twice the
+	default band size leading to unnecessary memory overflows there. This
+	commit fixes that. Now the bands are distributed more evenly and
+	cannot exceed the default size.
+
+	Now the magic number 8 is really suitable for rather simple European
+	scripts. For complex Chinese logograms the magic number should be 13
+	but that is subject for another day.
+
+	* src/smooth/ftgrays.c (gray_convert_glyph): Revise sub-banding
+	protocol.
+
 2016-07-07  suzuki toshiya  <mpsuzuki@hiroshima-u.ac.jp>
 
 	[mac] Fix Savannah bug #48417.
diff --git a/src/smooth/ftgrays.c b/src/smooth/ftgrays.c
index f0e380e40..12df14dc4 100644
--- a/src/smooth/ftgrays.c
+++ b/src/smooth/ftgrays.c
@@ -1893,27 +1893,28 @@ typedef ptrdiff_t  FT_PtrDist;
   gray_convert_glyph( RAS_ARG )
   {
     TCell        buffer[FT_MAX_GRAY_POOL];
-    const int    band_size = FT_MAX_GRAY_POOL / 8;
-    gray_TBand   bands[32];
-    gray_TBand*  band;
-    int          n, num_bands;
+    TCoord       band_size = FT_MAX_GRAY_POOL / 8;
+    int          num_bands;
     TCoord       min, max, max_y;
+    gray_TBand   bands[32];  /* enough to accommodate bisections */
+    gray_TBand*  band;
 
 
     /* set up vertical bands */
-    num_bands = (int)( ( ras.max_ey - ras.min_ey ) / band_size );
-    if ( num_bands == 0 )
-      num_bands = 1;
-    if ( num_bands >= 39 )
-      num_bands = 39;
+    if ( ras.count_ey > band_size )
+    {
+      /* two divisions rounded up */
+      num_bands = (int)( ( ras.count_ey + band_size - 1) / band_size );
+      band_size = ( ras.count_ey + num_bands - 1 ) / num_bands;
+    }
 
     min   = ras.min_ey;
     max_y = ras.max_ey;
 
-    for ( n = 0; n < num_bands; n++, min = max )
+    for (; min < max_y; min = max )
     {
       max = min + band_size;
-      if ( n == num_bands - 1 || max > max_y )
+      if ( max > max_y )
         max = max_y;
 
       bands[0].min = min;