The only problem with that is that it can put an unnecessary strain on
the server as *everything* is then sent through the ASP.NET engine.

Another solution is to create a Hats folde and add a default.aspx file
to it. This file does not need to do anything as the engine will
redirect to the real URL anyway, it's just there to get ASP.NEt to
process the request.

This is only practical if you have a smallish number of folders you want
to use. If you many, or if they change regularly, then this may not be
practical.

You could consider using URLs like /Hats_ReallyCoolHat.aspx which will
save you the hassle, and be better for the search engines as it looks
like a top-level folder instead of a second-level one like you
suggested.

HTH