Maybe something more like one of these?
http://www.knittingfever.com/c/louis.../4/?pattern=51
http://www.ravelry.com/patterns/libr...d--slouchy-hat
http://knittingonthenet.com/patterns...iralstripe.htm
LOL looking for striped hats is kind of fun! I guess narrowing the parameters could be helpful.
Here's a hat much like the one I linked to done up in red and white. I'm thinking of doing it Red Heart With Love in Berry Red and White.
http://knitting.about.com/od/hatpatt...triped-hat.htm