How to clear up SMS space? I just got a notification that I can't receive an SMS because "the space/memory was full". Which is it, the internal or SD space, and what's the best way to free it up?

Note - I just installed a bunch of apps, so I'm suspecting it's the SD.
I got this some time ago, and even after deleting all of messages (I back them up to my Gmail) I got the same thing. The problem was that when the internal memory fell below 22M or so (I forget exactly), this message appears. The SMS themselves take up very little space, so deleting them had no effect.

You may also be suffering from this bug, as I was, which it is important to know about: 
http://code.google.com/p/android/issues/detail?id=4991