Convenience is what you should be going for. If you're able to generate a short url for convenience, the chances of someone signing up later rather than saying "Signup just to try? fuck it" are higher.

Hell, when generating the url, just make a call to the api at http://tweak.tk so that you can display the short one side-by-side with the long one. Provided your codebase is well formed, a change like that should not be astronomical.

(P.S. Tweak.tk is really awesome. At least check it out.)