A bone screw (1) is provided having first (5) and second (7) threaded portions of different diameter separated by a middle portion (6) that is unthreaded so that the bone screw may be inserted into a pair of adjacent bone fragments and used to compress the fragments together by driving the screw into a hole drilled in the fragments. An installation tool (15) is also disclosed for threadably engaging one end of the bone screw and is used to initially drive the screw into the bone hole. Thereafter, a screwdriver (16) is inserted through the tool and into engagement with a recess (11) in the bone screw and may be used to drive the screw fully into the bone and to separate the bone screw from the installation tool.