Apparatus and methods for phacoemulsification combine a phacoemulsification needle having an offset feature with a handpiece capable of producing longitudinal motion to create a hybrid phacoemulsification effect that is more efficient than conventional longitudinal handpiece-needle combinations and has been demonstrated under certain conditions to be more efficient than needles used with handpieces providing torsional motion. The phacoemulsification needle is of the type having a hollow passageway that terminates in a straight needle tip formed off-axis from the passageway, allowing the needle tip to move eccentrically when the needle is subjected to longitudinal vibratory motion. The tip may be flared or may be coextensive with the needle body. The tip may also be angled with respect to the needle body. The aspiration passageway formed through the needle body may be positioned or shaped to be off-axis from the needle body axis.