Unless it's a one piece base, don't use shims. Don't. The scope is a rigid tube and rings are just tubes that clamp to the scope. They're even more rigid. They both need to be on the same centerline and if they're not, the scope has to bend. Shim one base of a two-piece set, the rings will be out of alignment. Shim one ring, same thing. Clamp down on a ring that's not lined up with the other, you also get an edge cutting into the scope. Lapping rings is a minor help but the problems you're talking about are major. Just use Burris Signature rings and don't screw around with other stuff. The Burris website has a beautiful explanation of what I said above.
Sight or scope adjustment.....the rear sight/eyepiece/reticle is adjusted in the direction you want bullet impact to go. To move the point of impact down, adjust the elevation down.
