An irrigation sleeve (78) for use with a surgical system (40) comprising an irrigation source (68), a surgical tool (44) having a tube (60) to support a cutting accessory (52) having a head (64). The irrigation sleeve (78) comprises a body (86) extending between proximal and distal ends (86P,86S). A first lumen (88) formed in the body (86) receives the tube (60) with the head (64) adjacent the distal end (86S). A second lumen (90) formed in the body (86) spaced from the first lumen (88) comprises different proximal and distal regions (92,94). The proximal region (92) extends from an inlet (96) for fluid communication with the source (68), to a transition (98). The distal region (94) is spaced out of fluid communication with the first lumen (88) and extends from the transition (98) to an outlet (100) to direct fluid adjacent to the head (64).
