If you have a gradient on a mask for a strong change in an image, like you would use for a vignette, you may see banding on your image. Smooth transitions in gradients are often subject to banding, especially if they have been manipulated after being rendered.
First, check your image at 100% (actual pixels) to see if the banding is still there. Even with the latest versions of Photoshop, Lightroom and Elements and OpenGL Drawing Optimization available (depending on your video card) it is possible to see some artifacts introduced into your images if viewed at lower percentages on screen. On my machine they show up first as banding in gradients, which disappear at 100% view. On some percentage views I also get a white band of pixels around the image perimeter. It is disconcerting to see those show up at all as we get more and more used to seeing a nearly perfectly rendered image at any percentage. But it happens.
If there is any banding in your gradients at 100% view, a little noise can help solve the problem. Go to Filter | Noise | Add Noise and put 1 or 2 percent noise onto the gradient depending on the file size. This should help the banding disappear, and that small amount of noise will not be visible in a printed image. I have occasionally found that doing this and blurring the noise by .3 pixels (3 tenths of a pixel) has a nice calming effect on a gradient, especially a strong gradient on a Black and White image. That is also a good argument for working in 16 bit mode for Black and White images where you are more likely to use strong tonal modifications. It also argues for making as many modifications as possible in the raw converter or Lightroom before editing in Photoshop or Elements.