I have a 7600 Rem very similar to your 760 and I understand they are having the same problems with rattle. The rattle which I first noticed a few years ago didn't bother me because I usually hunt from a stand, but I did notice that my groupings at the range were acceptable but getting worse during the same time frame. It was apparent that the forend was making solid contact with the barrel and I thought this might be affecting accuracy. When I removed the forend I noticed the same change in the finish at the base of the barrel described by jawshbawx. A closer look at the forend revealed that one small area of wood at the base of the forend was worn away on one side. I might not have noticed it until I looked at the opposite side of the forend and saw the difference in the finish and shaping of the wood. I thought I'd try putting several layers of electrical tape directly over the worn area as a trial to get an idea of how much buildup I'd need and the problem seemed to be corrected temporarily. For the final fix I used some Plastic Wood in layers to match the tape buildup. I actually went a little thicker since it's easy to sand the Plastic Wood. It solved the rattle but I haven't been to the range yet to see if it solved my other problem. I'll try to post some pics to give a better indication of the above.