"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..."

There are other problems you can run into with 2 piece bases.

I have attached both bases and tightened the one of the rings to the base, leaving the other one free.

In some instances, with one ring tightened, there wil be a space between the other base ring. If you do not shim this base, the scope tube will bend when you tighten the ring tight into the base.

I have noticed it more often with the rear base. It probably happens because of manufacturing tolerences in both the rifle receiver and the bases and rings.

It occurs frequently when sporterizing Mauser 98s and other military actions if you take some metal off the rear receiver ring.