I tried the compound and wax from walker briar works also. I didn't find the compound all that useful, but I was trying to restore some pretty gnarly stems from estate purchases. The wax is pretty nice and does a pretty good job of maintaining the stem.
Mr. Clean Magic Eraser does a pretty good job of removing oxidation, but again, not really tough stuff. It is great to getting right into the corner of the lip though.
Micro-mesh sanding pads work very well, but you have to be careful. They are hobbyist sanding pads that go to extremely fine grit. With a little patience, you can have the stem nearly shining prior to waxing. They will removing stampings/logos from the stems if you get careless.
I have also used the micro-mesh pads to restore the briar itself. Works well for removing varnish from a smooth pipe or for cleaning up the rim a bit. Again...need to be a bit careful.