A firearm scope mounting system where recesses and protrusions in the scope ring precisely mate with like recesses and protrusions in the telescopic sight tube itself to prevent the scope from moving fore and aft as well as rotationally under recoil or other forces. Additionally, these mating surfaces can be designed in such a way that the crosshairs of the scope are perfectly aligned horizontally and vertically when the scope is installed in the rings. The method of attaching the scope rings to the base and the base to the firearm is not the subject of this patent claim.