I've used black chunky yarn with sc all over to make the hat harder. As the hat was too snuggy, I changed the initial plan to put ribbon around it to a crochet band which is more stretchy. I tied the bow with a ribbon so that it is not too thick.
Here's how it looks like when I model it. It looks ok for my first 'not quite there yet' Fedora= Fydora hat.
Later will try to make a better & slightly bigger one for guys =).