(Thinking about it more carefully, I doubt 15 bits would be a huge improvement. There would still be a visible gap between the poor approximation to solid-808080 attained by rounding it up to solid-848484, and the better approximation attained by dithering between 848484 and 7b7b7b. You wouldn't get the various exciting off-greys any more, but the visible dividing line would still be there.)