Many thanks to all those that posted their ways to shine aluminum rims. As I anticipated, there was some new methods and products I hadn't thought of so I'm glad I asked. A few days ago I got out my Simichrome polish and started in a small area to see how it would work. I soon discovered that the rim's oxidation went just deep enough that I thought I should sand the rim first to make its surface a bit smoother. I have all kinds of sandpaper grits because I paint frames. Now I'll probably start with 800 grit and see how much finer I meed to go. I hadn't thought of using a Scotchbrite pad and had forgotten about Mothers polishes.