The first cutting edge can advantageously remove a large burr from the edge of a drilled hole with high effectiveness, because of the particularly aggressive cutting action of the first cutting edge. The following inclined second cutting edge advantageously allows precise chamfers to be cut, i.e., the surface and the angle of the counter bore can be precisely maintained, independent of the wear on the cutting edges. A control surface located adjacent to the cutting edge in the forward region enables a precise control of the cutter.