Scope mount on a Contender barrel is off in windage by roughly 50 m.o.a., mounting a scope that can adjust about 35 m.o.a. so it's about 15 m.o.a. shy of being able to be sighted in. I think I can shim the mounts to gain about 4 to 6 m.o.a., still not enough. So how can I adjust the mount sufficiently?

This is not the type of mount with windage screws on one end. Since shimming won't work it seems that the only choice is to rearrange the rings to see if there is another combination of ring positions that manages to align better.

That's severe. What about Millett Angle-Loc rings? I don't know how much they can adjust but you can get something out of them.

If it is the screw holes in the barrel that are off that much I would contact T/C and see if they would help (replace or fix). Other than that, you may want to try the Burris Signature rings.

But the rifle is so incredibly accurate there is no way I was going to send it back. My solution was the Redfield Jr or Leupold Mount (I forget which one it is) with rear windage screws. That solved my problem.

I have a 1895 SS that has the same problem. The windage and elevation are off. I can sight it in but it requires about all of the scopes internal adjustment.

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The bottom of the mount is concave and sets solidly on top of the round barrel, so it could be the concave part that is off.

I think this particular mount actually is a Burris.

I'm going to try swapping the rings around, then might even try shimming. But the shimming will require 2 thicknesses of soft drink can in each ring which might not even fit.

Either comes with shims or its adjustable. I forget exactly which base and rings it is but I've used one in the past on another rifle besides my Guide Gun. It definitely lets you add in some windage adjustment when you mount the scope. Now I'm curious because I know I have a scope mounted on something in the rings he mentioned...I'm gonna figure it out....

It uses shims inside the rings to change windage and elevation. I did have a scope mounted in these and it worked well but I can't remember what it was for the life of me. https://ads.midwayusa.com/product/712472/burris-1-signature-ring-pos-align-offset-inser...

I had a scope in a Duo-mount for years (they really are kind of crappy) and it squashed the tubes some. It worked fine in that mount, but I couldn't use it in any other type mount as it was miles off.