I always like to do anti-brainstorming or anti solution, not quite sure how they call it. But you basically write down the worst things that could happen/ what you absolutely don't want to have associated with your design (seriously, the worst!).
That usually gives another fun and more open insight and from there it's sometimes easier to figure out what you actually want your design to express. I always find it to be a different level of brainstorming, as my thoughts always wander from the purely visual zone to the more abstract meaning behind. I have never tried it with a logo though, but I should think it'd work just a well :)