Irish crushable: http://www.hannahats.com/. I have a gray one very similar to that shown at the top of the page. It's a Hanna hat imported from Donegal and purchased a couple of years ago from Meyer The Hatter on St. Charles Avenue in downtown New Orleans.

Unaccustomed as I am to the northern winter, I make it a point to keep my head covered whenever I venture outdoors. I have a nice collection of baseball caps, but find myself using this one tweed cap almost to the exclusion of all other alternatives.

When I go indoors and take it off, find it very convenient to stuff it into the sleeve of my jacket. Because it truly is "crushable," it is completely unaffected by this treatment. It's formal/dressy enough for most occasions, and comfortable even in the most informal circumstances.