Abstract: A rifle scope mount system includes a base having forward and rear mounting blocks attachable to a rifle barrel. Forward and rear scope clamp rings are attachable to a telescope engagable with the forward and rear mounting blocks, respectively, to mount the telescope to the gun. The forward mounting block has a female dovetail recess for rotatably receiving a male dovetail stud extending from the forward clamp ring. The rear mounting block has a flat upper surface. The rear clamp ring has a flat lower surface which is coplanar with the flat upper surface when the male dovetail stud and the female dovetail recess are mated. A first windage screw is threaded into a first hole in a first side of the rear mounting block so that its head extends above the flat upper surface and engages one side of the rear clamp ring. A second windage screw is threaded into a second hole on the opposite side of the rear mounting block. The head of the second windage screw has a flat surface.