Methods for automatically maximizing blood oxygenation saturation or maintaining blood oxygen saturation levels in adult patients having an oxygen requiring pulmonary disease and infant patients having underdeveloped lungs, within a specified range of values. In one embodiment, the method includes energizing a valve to deliver oxygen to the patient at a first rate and measuring the associated average oxygen saturation level of the patient. The method also includes deenergizing the valve and energizing another valve to deliver oxygen to the patient at a second rate and measuring the second average oxygen saturation level of the patient. A dominant valve, the valve associated with the higher average oxygen saturation level, is identified based on the measured oxygen saturation levels and then energized to deliver oxygen to the patient, thereby maximizing the blood oxygen saturation level in the patient.