rosalindr; if you get a small screwdriver, and push the mirror all the way to the inside, you can tighten up the mirror. Just screw it in, and it will tighten up the glass element so it doesn't shake. If you really want it to last, put some locktite on the screw. Hope that helps.
I bought a Black & Decker power screw driver with four trays of driver heads (highly recommended ). I tried to screw the mirror tighter at first, but that didn't seem to work. So I tried to unscrew it. The screws turned and loosened up, but not enough to come off. So I pried the mirror off, and low and behold, it was held on by riv-nuts. Now I have two big holes where the riv-nuts popped out. I'm going to follow Dan's method of reattaching it. Those riv-nuts are too hard to take off. Thanks for all the help. Roz