Varis gives a very good, easy-to-understand introduction to banding problems, and then suggests the use of PS's splatter filter to break up the banding.
The spatter filter is a more effective version of the standard advice to add a slight bit of digital noise to the sky to break up banding. If you happen to have a good film grain simulator, ie, one that allows you to change the size of the grain, that's even better than the splatter filter, but the best film grain simulators (eg, Imagenomics' "Real Grain") are commercial plugins and are not free.
One of the other important take-home messages in his video is his discussion (towards the end of the video) of how smoothing filters, instead of helping with banding problems, often can actually make banding worse.
It's well worth watching the entire 20 minute video.
16 bpc should be your SOP whether you anticipate banding or not. It's also incredibly useful if you have to lift dark shadows.
The other thing you have to worry about is the bit depth of your video card and monitor. Often (especially in the past), you may be dealing with high bit depth images, but they show banding because your video system doesn't even really use 8 bpc. Some dither the last bit or two for cost or refresh rate reasons, so you might see banding when it really doesn't exist.
That video on splatter technique for banding did the trick! Thanks Tom!
Lee Varis' video really explains it best and as Tom said the 20 mins is worth it if you have this issue!
Add the splatter filter to a duplicate of the main image then with a layer mask brushed back the areas which didn't have banding like the shore line etc. See how much it cleaned up the top of the picture.
... and then described the techniques we have been discussing in this thread and this forum.
I realize it was probably just an oversight, but in technical literature like this, instead of referring to the "research you have done", a citation or even just an informal mention of the forum that first pointed you to this solution is considered standard professional / collegial courtesy and certainly is *always* appreciated. ;-)