An instrument (10) having a working section (11) that terminates in an end zone (12) having a pointed tip. The end zone (12) has, on the one hand, a conical guiding section (13) which ends in a tip. This guiding section (13) has a tip angle of between 10° and 60° and, on the other hand, an angular cutting section (14) adjacent to the conical guiding section (13) which has three cutting edges (15). The angular cutting section (14) extends over a certain length and is located intermediate between the conical guiding section (13) and the working section (11). The angular cutting section (14) has a cross-section that progressively increases from the base of the conical guiding section (13) over at least a portion of its length.