Using a collet bullet puller, you do not have to tighten the collet around the bullet as tight as you may be doing it. As far as the ring affecting the accuracy of the pulled bullet, that would depend on the depth of the ring. usually any type of damage to the bullet would cause it to loose accuracy, but the collet is probably not making much of a dent and I do not believe that you would notice much of a change. One other thing would be to use these for target practice or load developement or just to target shoot/plink, but I think you will find that since the ring is all the way around evenly and should not be more that a couple thousanths deep, I do not think that you will have a problem with them. Try shooting them on paper for accuracy!
Again, try using less pressure on the bullets when pulling them. Mine have never had a ring on them after pulling, and I have even pulled Barnes "coated" bullets....JOHN /ubbthreads/images/graemlins/grinning-smiley-003.gif