A method of performing peritoneal dialysis includes: (i) locating a supply of fresh dialysis fluid above a patient's peritoneal cavity; (ii) locating a drain or a drain container below the patient's peritoneal cavity; (iii) connecting a supply line to the supply of fresh dialysis fluid and the patient's peritoneal cavity; (iv) connecting a drain line to the patient's peritoneal cavity and the drain or drain container; (v) pneumatically opening a supply line valve during a fill cycle; (vi) gravity filling the patient's peritoneal cavity with the supply line valve open during the fill cycle; (vii) pneumatically opening a drain line valve during a drain cycle; and (viii) draining the patient's peritoneal cavity with the drain line valve open during the drain cycle.