Ernie pretty well summed it up. Care of the threaded portion is absolutely critical. It doesnt take much to wang it to the point of no return.

On this old Tudor project, I polished some vintage Aj's, and added some etched inserts on a whim.

To get the mirror finish you have to back up a step or three. For the really nasty finished impersonator examples you may have to go down to 320 grit paper to correct any ugly machining. Normally on a vintage Aj's, you can start at 600 then go to 1200. Just chuck them in your dremel and take your time. A little water or lube helps keep the paper cutting and your fingers from burning. The trick is to keep the paper moving and adjust it frequently, so you dont cut concentric lines or grooves into the rim. Bzzzzt, then adjust. Bzzzt, then adjust is the ticket. Wash out any excess grit. Add little medium rubbing compound on a Q tip and let it eat in the rim. I use Mothers Mag Polish for 1:1 alloys, so it's on hand. Any metal polish will do. Finish by buzzing the rim on a little rolled up piece of linen or terry cloth to get the luster. I finish with some regular old automotive wax to help forestall oxidation.