A bit for removing a broken fastener comprises a tip from which extend two or more notches separated by scraping surfaces formed from two-sided frusto-conically-shaped regions. The scraping surfaces are bounded on one side by a cutting edge and on the other side by a non-cutting edge and are configured to cut into the fastener when the bit is rotated in a direction opposite to the fastener's direction of engagement. Specific embodiments include configurations where the cutting edges extend at different angles with respect to the bit axis and where the scraping surfaces comprise a plurality of serrations.