Abstract: A tool for engaging a damaged or mutilated hexagonal socket in a threaded fastener, or the like, so that sufficient torque may be applied to the fastener to effect unthreading and removal thereof from a part with which the fastener is engaged. One end portion of the tool is tapered and hexagonal in cross section, thereby providing three pairs of opposite sides. Each side is tapered inwardly by a predetermined angle which permits the sides of the end portion to wedge against respective walls of the socket when forcefully driven therein. The opposite ones of each pair of sides of the end portion are spaced by a gauge width which, together with the taper of the sides, coact to prevent the end portion of the tool from bottoming in the socket when the tool is fully engaged in the socket.