A lavage unit including: a handpiece including a proximal located handgrip and a distally located barrel; an irrigation tube that extends from a source of irrigating fluid to the handpiece; a pump (560, 620) disposed in the handpiece to which the irrigation tube is connected, the pump including a bellows (560, 620) that defines a pump chamber (576, 624) and an outlet, the bellows configured so that, when the bellows is reciprocated, the bellows draws fluid from the irrigation tube into the pump chamber and then discharges the fluid out of the pump chamber through the outlet; an inlet valve (582, 634) that allows fluid flow into the bellow pump chamber (576, 624) from the irrigation tube and that blocks fluid flow from the pump chamber towards the irrigation tube; an outlet valve (584, 634) that allows fluid flow from the bellows pump chamber (576, 624) into the outlet and that blocks fluid flow from the outlet into the pump chamber; a motor and linkage (602, 608) disposed in the handpiece for reciprocating the bellows; and a tip assembly that extends forward from the handpiece, the tip assembly including an irrigation tube that receives the fluid discharged from the pump outlet for discharge towards the tissue to which the lavage unit is applied, characterized in that: the pump further includes a section (566, 628) formed from compressible or flexible material that defines a supplemental chamber (568, 630) that is either located between the irrigation tube and the pump chamber (576, 624) or between the pump chamber and the pump outlet; when the supplemental chamber is located between the irrigation tube and the pump chamber, the inlet valve is located between the supplemental chamber and the pump chamber; when the supplemental chamber is located between the pump chamber and the pump outlet, the outlet valve is located between the pump chamber and the supplemental chamber; the linkage (602, 608) is connected to said pump so as to alternatively compress the bellows forming the pump chamber (576, 624) and the material forming the pump supplemental chamber (568, 630) and so that during the movement of the linkage the said valve (582, 638) located between the pump chamber and the supplemental chamber reciprocates with the linkage. a handpiece including a proximal located handgrip and a distally located barrel; an irrigation tube that extends from a source of irrigating fluid to the handpiece; a pump (560, 620) disposed in the handpiece to which the irrigation tube is connected, the pump including a bellows (560, 620) that defines a pump chamber (576, 624) and an outlet, the bellows configured so that, when the bellows is reciprocated, the bellows draws fluid from the irrigation tube into the pump chamber and then discharges the fluid out of the pump chamber through the outlet; an inlet valve (582, 634) that allows fluid flow into the bellow pump chamber (576, 624) from the irrigation tube and that blocks fluid flow from the pump chamber towards the irrigation tube; an outlet valve (584, 634) that allows fluid flow from the bellows pump chamber (576, 624) into the outlet and that blocks fluid flow from the outlet into the pump chamber; a motor and linkage (602, 608) disposed in the handpiece for reciprocating the bellows; and a tip assembly that extends forward from the handpiece, the tip assembly including an irrigation tube that receives the fluid discharged from the pump outlet for discharge towards the tissue to which the lavage unit is applied, the pump further includes a section (566, 628) formed from compressible or flexible material that defines a supplemental chamber (568, 630) that is either located between the irrigation tube and the pump chamber (576, 624) or between the pump chamber and the pump outlet; when the supplemental chamber is located between the irrigation tube and the pump chamber, the inlet valve is located between the supplemental chamber and the pump chamber; when the supplemental chamber is located between the pump chamber and the pump outlet, the outlet valve is located between the pump chamber and the supplemental chamber; the linkage (602, 608) is connected to said pump so as to alternatively compress the bellows forming the pump chamber (576, 624) and the material forming the pump supplemental chamber (568, 630) and so that during the movement of the linkage the said valve (582, 638) located between the pump chamber and the supplemental chamber reciprocates with the linkage.