Are you using a nylon cap?
I've been wearing these mens satin skull/wave caps under everything, including wigs, for over a decade!
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I've found that they do a good job of keeping my hair moisturized underneath. I use it inside out so that the satin part is touching my and the seams face out, away from my hair. And, it's not as tight as a nylon cap so I don't feel like my circulation is being cut off. Lol
Also, have you tried whole head baggying under the nylon cap or even overnight before putting on your nylon cap? Maybe that will help.