Abstract: The cutting edges (16) of a 3-toothed countersink bit (10) lead slightly in the direction of rotation by an amount (t). The rear face (38) of the head (40) of a detachable pilot (30) is concave so as to fit snugly over the forward end of the bit (10). Lubricant is supplied via a bore (28), flats (44) on the pilot shank (32), a chamber (42) at the mesal end of the shank (32) and notches (46) in the tip of the bit to the spaces between the teeth (14).