I have found that the best way to get the "whole" rim clean is to remove it. the backside always seems to get slight surface pitting. If you don't want to remove, then get yourself a flexi head brush and go to town. i am not going to suggest a product, since there are thousands to choose from and everyone has a preference. Just make sure to not use any abrasive cleaners, they leave fine scratches that you cannot see until its to late.