Amen to that, ESPECIALLY if you have more than a few bullets to pull.
If you can afford to possibly lose the bullets, you can use the "poor man's bullet puller collet": your press and a pair of pliers. Remove any die from the press. Raise the loaded round up through the top of the press. Grip it with a pair of slip-joint pliers. Lower the ram. The pliers will jam in the die opening, gripping the bullet very tightly. Pop! Bullet pulled.
Very thin-jacketed bullets may or may not be ruined by this method. I use the worst ones as foulers or plinkers. But, surprisingly, most will shoot just fine even with gouges, grooves and dings in the jacket - at less than hyper-speeds, anyway.