A torsional ultrasound surgical hand piece lessens or eliminates chatter from lens material by imparting a twisting, rotary motion to a tip of a phacoemulsification needle at a resonant frequency in excess of 32 kHz. The hand piece has a horn that is designed to operate at an elevated frequency while maintaining size constraints for hand-held ophthalmic instruments. Optionally, heat generation is reduced either through the use of a polyimide tubing situated between the needle and the infusion sleeve, through the use of thermal watch to prevent overheating at the incision, and/or through the use of a bypass hole in the needle that diverts flow under suction into the needle via the bypass hole instead of exiting through an irrigation opening in the infusion sleeve when a tip port is occluded by lens material.