Ed,
I've got 5 scopes mounted in Burris Sig. rings that have 50 mm objective lenses. They are all in med. rings, none of them have required the highs.
They are on 4 Savages and a Remington that have barrel contours that range from a #5 Pac Nor to a big M24 Rock Creek that is .900 @ the muzzle.
Chris