My kids bought me a hat made by Columbia (the outdoor sports wear company) that looks like the Tilly but is made out of a very light weight fabric with a ventilation type weave all around from the flat top to the brim. It also has an adjustable elastic headband pull cord (for those 20 knot days) and a chin strap.

The nice thing about it is when going upwind in a good breeze, the upwind side will fold up so you can see the puffs comming. It's very light, keeps the sun off your ears, neck and out of your eyes, and dries quickly. I don't know what it cost, I'm guessing about $20? (Maybe on sale at Dillards?)