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The problem with shimming one ring is that it results in the bottom of the rings no longer being on the same level. Your surface area when you lock the top of the ring down will be reduced to one edge of both rings. It may be slight, but it will be there. You couold put the scope tube in a bind.
One thing you may try is to turn the scope sideways and see if you have more windage adjustment than elevation. Probabaly not on a better scope but with the inexpensive models you never know.
BTW, if you need more elevation, I think you would want to lower the front of the scope, not raise it.
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