An instrument for drilling a hole for a bone screw comprises a shaft having a primary drill fluted portion, a shank, and a middle portion there between. Part of an outer surface of the shaft's middle portion is non-curved. A sleeve surrounds the shaft. The sleeve has an inner surface that is complementary to the outer surface of the shaft's middle portion such that the sleeve slides with respect to the shaft. The sleeve's inner surface contacts the outer surface of the shaft's middle portion at the non-curved part such that the shaft can transmit torque to the sleeve. A countersink drill bit is provided at an end of the sleeve proximate the shaft's primary drill fluted portion. A locking mechanism selectively holds the sleeve in a fixed position with respect to the shaft, locating the countersink drill bit at a selected position with respect to the shaft's drilling end.
