I don't know how small you want to make your jump rings, but if you're making them to solder and not in HUGE quantities, may I suggest the method I was recently taught? Wrap your wire around a wooden dowel, clamp it in a vise, and saw through one side (you can go into the wood, no problem) with a very fine (4/0 or finer) sawblade. You barely lose any metal and you end up with very flush edges ready to solder.
-- KarenK Desert Dreamer Designs