Ah okay, that's never an issue for me. I don't use cotton handwraps, they need to stretch, and I disliked the Hayabusa handwraps I once had because they were too thick, as well as Le Roys. Apart from that I've been fine with any and all handwraps I've used just so long as they stretch.
Btw did you notice your face is in the OP now? Albeit wearing a facesaver, lol