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I have a polystraw that's lasted for seven seasons, a Riverz Delta:
I prefer fedora style, wanted straw and can't abide the look of a Tilley (more importantly, neither can my wife). It's a fairly open weave, so cool, has a sweat-wicking band and is nearly indestructible. It can be dunked to cool down, washed with soapy water and a brush, sat on, shoved in a gear bag, etc.
It does have a 3" brim - not sure why you'd want only a 2" brim, that doesn't offer much sun protection, especially on the back of the neck, ditto for ball caps unless you wear the curtain across the back.
Orvis has a version that is a nice shape, but the brim is floppy compared to the Delta (which has a wire in the brim edge to retain its shape against wind). I have one that I use for hiking, it works well in the rain. The brim on this one is about 2.5", I think:
PS polystreaws float, per the comments below....
...... dirt cheap , excellent used ones around for a buck or two at flea markets , Goodwill stores , etc. .
I like a thin corduroy in the winter .
There was this one I guess it's called combat or bush style hat that I saw at a tackle shop that I wish I would have sprung the $25. for but didn't . It was the only really decent summer full wide brim that ever caught my interest . Flexable , floppy brim (yet kept it's shape well) , open mesh full around side riser (solid top) , and exremely light . Unfortunately that brand was replaced by another the following year and have never found another like it .
I've always worn the type with the stand up front panal (maybe called farmer , truck driver style ??) , which are becoming more and more difficult to find now a days . Seems like "all" the new ones today are the round tops and have sponsor logos or weird color patterns I don't favor . Come to think about it , baseball "league" caps have probably always been the round tops (not the stand up front panals) .
When it's raining hard enough I slip on my lightweight breathable rain gear , the hood fits perfectly over the ball cap ... try that with most other hat styles and it's either impossible or very uncomfortable .
The last thing I'd want to be doing is worrying where my $100.-$200. hat has gone off to ... just like expensive sun glasses . Oh sure , quality has it's place , but not at the expense of carrying a ball and chain around with you .
Hat "advise/help" , tap into the knowledge (hard to think anyone could need it though) , but decent enough topic for discussion ... guess it's just a sign of the times :-)
It's currently available at Sierra Trading Post for $22 - if this is the one, you should buy out your size (I'm a hatophile as well, still kicking myself for not buying a certain polystraw I saw a couple of years ago which was discontinued...)