A dialysis machine includes a dialysis instrument having a pump actuator and first and second valve actuators, and a disposable cassette operable with the dialysis instrument, the disposable cassette including a pump portion operable with the pump actuator, first and second valve chambers operable with the first and second valve actuators, the first and second valve chambers communicating fluidly with each other, at least the first valve chamber communicating fluidly with a compliance chamber, the compliance chamber negating a first backpressure due to a pneumatic closing pressure used to close the first valve chamber to help to ensure the pneumatic pressure applied to the first valve chamber will close the first valve chamber against a second backpressure from an existing closure of the second valve chamber.