A fluid delivery system comprising a pump arranged to draw fluid, in use, from a reservoir (1) and dispense it through a dispensing tube (4), the pump comprising a cylinder (21) in which a piston (22) is reciprocally movable; an inlet into the cylinder; a one-way inlet valve (17) for controlling flow through the inlet; an outlet from the cylinder and leading to the dispensing tube; and an outlet valve (27) controlling flow through the outlet, wherein the piston is arranged to selectively contact the outlet valve to maintain it open during the initial portion of its downstroke and to allow it to close for the remainder of the downstroke.