A medical fluid delivery machine including: a medical fluid pump including a pneumatically actuated pump chamber and first and second pneumatically actuated medical fluid valve chambers located respectively upstream and downstream of the pneumatically actuated pump chamber; a compressor for creating positive pressure air; and an accumulator storing the positive pressure air for delivery to at least one of the pneumatically actuated pump chamber, the first pneumatically actuated medical fluid valve chamber, or the second pneumatically actuated medical fluid valve chamber, the accumulator holding an elastic bladder that inflates under positive pressure air from the compressor, creating additional positive pressure that increases the amount of positive pressure air that the accumulator can provide.