Color banding occurs in AVI output.

If you compress color as 4:2:2, basically you average color in blocks of 4 pixels. This causes color banding in subtle gradients. If you use 4:2:0, the banding is worse. The solution is to introduce a little noise or grain in the footage. When you are stuck with 256 maximum luminance values and a color gradient that goes from something like 18 to 24 over an entire frame, there are only seven possible values for the frame, and without noise or grain, those are going to show up as 7 different lines. The noise/grain hides the lines.

Your best option when dealing with subtle colors is to set the project to 16-bit, add a little noise or grain, and then use one of the presets or a preset in the Media Encoder to render an H.264 4:2:2 deliverable for viewing on the net or in a media player. Unless you have a very good understanding of video codecs and compression algorithms, coming up with your own settings can often cause problems that the presets avoid. 

If you are rendering for further editing and processing, including re-compressing for distribution, it is always a good idea to render to a frame-based codec like ProRez at least 10-bit color. MPEG formats are unsuitable for production or archival masters. You don't want the codec to be predicting the movement of pixels between frames like MP4 formats do by default.