If you're working with 16 bit data, any banding you see is in your display system. Remember that the display pipeline from video card to monitor operates at 8 bit depth. That's where the banding happens!
Furthermore, this banding is cumulative. Calibration tables in the video card, a suboptimal monitor profile, the panel itself (many of which are actually 6 bit + dithering) - they all go on top of the basic 8 bit banding. The result can be highly irregular and colored banding. But it's all in the display system, not in the data.
Obviously, converting to 8 bit depth for output will reintroduce banding - but that's not what you're seeing now.
If this is a major concern, you may want to invest in a 10 bit capable monitor and video card.