Blurring one or more of the color channels does a better job for reducing or eliminating banding problems. Adding noise more to a comp which may be destined for Web delivery will only result in a poorer quality web version as compressors usually have a harder time compressing noise.
Use Effect>Channel Blur and increase one of the values to solve your problem. You can tell which channel needs more attention by looking at the individual color channels in the Comp Panel prior to applying Channel Blur.
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