Caddisman,
Pat has given you good advice. I only wish to add that this is another godo reason to obtain a CPL if you an afford it and qualify. It shouldn't be needed to excersize your right, it should be easier or at least cheaper to get, but in the end, it does make it easier to carry a firearm, concealed or openly. But yea, keep the shirt, sweatshirt, and jacket behind the pistol.
-jason r.