Actually, one of my very favorite hats is Outdoor Research's Seattle Sombrero ($56). It's a Gore-Tex, seam-sealed hat with stylin' adjustable brim. Unless the wind is really blowing the rain sideways, it does a great job keeping the rain off your head, neck, and shoulders. It's also light and stowable. The Marmot Precip Safari Hat ($29) is really very much the same thing, although it's a little lighter and uses a non-Gore-Tex laminate. There's absolutely nothing wrong with the Safari Hatit's an excellent buybut I just think the Seattle Sombrero performs better in almost all conditions.
By the way, I'm really a fan of Outdoor Research's Hat For All Seasons ($48), a short-brimmed Gore-Tex hat with a removable pile liner and ear muffs. It's the essential hat for cold conditions. I wore one up Denali when I climbed it some years back, and I basically never took it off. Great for Rainier, winter cross-country skiing, all sorts of things.
Does the bush burn brightly in this case?
The Seattle Sombrero is available from REI here.