Golf Hats

Question
I'm in the market for a floppy hat that I can permanently keep in my Sun Mountain carry bag.  I'd like something I can flatten into the bag but has some degree of style when I pull it out.  Any thoughts about not making me look like Bill Murray in Caddyshack?

Answer
Couldn't think of any right off hand then went to Google and entered "Roll-up hats" and got quite a few hits.  I wear a Tilley hat which holds it's shape quite well although I haven't tried folding it away in my golf bag.

Fairways and Greens,

John
www.golfnutts.com