I have the same problem, it stinks!
I would make a list of what you like in your psychiatrist. Do you like the way he guides you, is he tough, is he quiet, etc. Once you have that list, convert it into a series of questions, like an interview. I would then call them and see if you can set an interview session, 15-30 minutes. As the prospective doctor your questions and see how they react. You can also throw in an off the wall question like "if you were an animal what would you be?" It's always interesting how people react to unexpected questions. The answer really doesn't matter, it is how they respond verbally and non verbally to your question.

Also I agree with Kalaopi (?), if you are happy with your treatment regiment make sure you find someone who will not change it just because they can.

Good luck!