I have a 7x57 Remington 700 mountain rifle, one of the ones from the 1990's with the thin barrel. It shot in a general way, but not enough to satisfy me, sort of everything around 1.5 inch three shot groups. I thought it should do better. The barrel was free floated.
Just for the hell of it I tested it with a shim under the front foreend, about 1.5 inches back from the foretip: I put a rectangle of inner tube under the barrel there. Tightened the stock up again, and shot it. I got a half inch group, and have done ever since. I superglued that rubber where it was and left it. I only shoot three shot groups, but I have several in a row at half an inch, so I am satisfied.
I have tried this before, because I read about it in a Jack O'Connor book, but this is the only rifle to which it has made a significant difference.
