A handpiece having a single set of piezoelectric elements polarized to produce longitudinal motion when excited at the relevant resonant frequency. The piezoelectric crystals are connected to an ultrasonic horn to which a cutting tip is attached. The horn and/or the cutting tip contains a plurality of diagonal slits or grooves. The slits or grooves produce optimized torsional movement in the cutting tip when the piezoelectric crystals are excited at a second resonant frequency. Preferably, the two drive frequencies are not coincident, but provided in non-overlapping pulses.