Abstract: A tool for removing threaded fasteners such as screws and/or bolts having hexagonal recessed sockets formed in their heads, with the tool including an elongated broach polygonal in cross section, with a sleeve having a like cross sectional configuration slidably mounted thereon. The sleeve is provided at one end with a protruding insert head that is capable of being projected into countersunk bores so as to have facial contact with a countersunk hex head of a fastener, while the opposite end of the sleeve may be countersunk so as to provide a receptacle for receiving the protruding or exposed hex head of the fastener to be removed.