A multi-sleeve handpiece for performing phacoemulsification with a vibratory, ported needle and for cooling an exterior of an incision. The vibratory, ported needle breaks up and aspirates broken eye tissue. The handpiece has at least one inner sleeve that guides irrigation fluid to the eye and/or reduces friction between the vibrating tool and the surrounding rigid sleeve or tissues. The handpiece has an outer, cooling sleeve that is concentric with the inner sleeve and the needle and whose distal end has peak and valley formations. The cooling sleeve is collapsible to engage incision tissue with the peak formations and allow the cooling fluid to flow across the valley formations to cool the tissue via heat transfer.