Thank you all for responding. I know a picture is worth a thousand words but I am not able to post one without considerable help. My guitar is a ES295 with a Bigsby tail piece and whatever bridge that came with it. Nothing broke, it just fell over, scuffing the finish, which is far from pristine anyway. The adjusting bolts, with the knurled adjusting nuts, sit in pockets on the bridge plate. I am thinking that this set up wasn't designed with slippery strings in mind. With a little more modification I think my wood brace or bracket will take care of the problem, but it looks kind of hokey. I check it frequently and find it leaning occasionally, but it has fallen only the one time.