The hats seem to be designed for passport-photo-like avatars. Perhaps it would be better if you could choose where exactly it fits?
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Sorry, but right now that's not really technically feasible. We apologize for the inconvenience.
That said! Part of the fun of this event is how silly we're all going to look, and how we can tweak our gravatars to make the hats look as awesome as possible! So go with it, maybe bust out the Photoshop (or, if you're cheap like me, MS Paint) and, as Tim Gunn would say -- make it work!
Beginning with the 2013 hat season, hats may be manually positioned!
How to make your unicorn* happy in three easy steps:
* Alternatively, your face.