A lavage unit may include a handpiece configured to house a pump to which an irrigation tube is connected. The pump may include a bellows defining a pump chamber. When the bellows is reciprocated by a linkage, the bellows draws irrigation fluid from the irrigation tube into the pump chamber and then discharges the fluid out of the pump chamber through an outlet. The pump further includes a section formed from compressible or flexible material that defines a supplemental chamber. The linkage is connected to said pump to alternatively compress the bellows forming the pump chamber and the material forming the supplemental chamber. During the movement of the linkage a valve located between the pump chamber and the supplemental chamber reciprocates with the linkage.