Disposable refill units, and pumps for disposable refill units for foam dispensers are disclosed herein. Exemplary embodiments include a container for holding a foamable liquid and a pump secured to the container. The pump includes a liquid chamber formed between a liquid inlet valve and a liquid outlet valve. In addition, the pump includes a sleeve that is located at least partially within the liquid chamber. One or more liquid passages are defined at least in part by an area located between an exterior wall of the sleeve and a wall of the liquid chamber. The pump also includes a piston body having a head and a sealing member located at a first end of the piston. The sealing member forms a seal against the interior wall of the sleeve and the piston head moves within the sleeve to reduce and enlarge the volume of the liquid chamber.