"..........Again, this is INSIDE the rings? A shim would be under the mount and on top of the rail. Tape makes a lousy shim, BTW. ........"
Mine had the extra layer of tape under the scope, not the mount.
BTW, the best way to shim with dovetail type mounts is under the scope, not the dovetail. Reason being, under the scope the mount stays centered. If you shim under one end only of the mount's dovetails, because they are roughly at a 45 degree angle the mount will cant sideways just as much as it gets raised by the shims. And, as shim thickness increases, the shimmed mount has less gripping surface area therefore, doesn't have as strong a grip and can even dent/distort aluminum dovetails.
For shimming scopes I use the electrical "friction tape" available at hardware stores. It's very much like the cushioning tape that originally comes in the mounts, only a bit thicker. It shims and cushions at the same time. And with that type tape being sticky on both sides, the mounts don't have to be tightened close to the point of denting the scope tube to hold the scope in place. I've used it for all my scope mounting, even on slug firing shotguns which have way more recoil than any springer, and the scopes don't move in hot or cold weather.
Paul.