If you are pulling crimped military bullets, you may want to invest in a collet-type puller that fits in your press. The combination of crimp+sealer often is a toughie to pull with the hammer-style puller.
Two things: 1.) As a follow-up to what Majorlk said, if the bullets are crimped or lacquer sealed (think military .45 ACP ball ammo, you can break the seal by running each round through a reloading press with the seating die in, set just low enough to push the bullet into the case slightly to break the seal. After that, use the bullet puller and bang away and you'll get the bullet out much more easily. 2.) I put a cotton ball in the bottom of the tube, to save the point of spitzer-type rifle bullets. Works well. This is not much of a factor with pistol bullets, though.
No danger of firing the round, but if I have many bullets to pull I much prefer the collet type. It is faster and takes less effort. I second the advice to adjust the seater so that the bullet is moved if pulling from military rounds.
I wouldn't be without both a kinetic puller and a collet puller.
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