This invention can be embodied as a wearable self-contained device that provides energy-efficient Positive Airway Pressure (PAP) to treat Obstructive Sleep Apnea (OSA). This device includes a primary airflow member and a bolus airflow member which operate together in a coordinated manner to provide just the right amount of pressure that is needed at any given time in order to keep the persons airway open in the most energy-efficient manner. The bolus airflow member can accumulate energy over multiple respiratory cycles and use this energy to release a bolus of air when needed. Energy efficiency is particularly critical for wearable self-contained Positive Airway Pressure (PAP) systems that a person can wear on their head without a tube connection to a bedside unit or a continuous wire connection to an external power source.