Alternatives to Crib Bumpers?

Lisa
I just started putting my 2 month old baby into her crib. She squirms a lot as she sleeps and is constantly waking up screaming because she has banged her head into the crib. It doesn't matter where I lay her in the crib or which direction, she always find a side with her head. I know I shouldn't put a crib bumper in, but is there something else that I can use that soften the blow when she hits the side? She also won't keep hats on. I tried those when I first brought her home to keep her warm and she takes them off/ squirms so much they come off.