The method involves repeated measurement of a flow of breath during the operation of the continuous positive airway pressure or CPAP device and determining at least one respiratory event from the measured time variation. A respiratory event represents an indication that the pressure from the CPAP device is too low. It involves slow, quasi-ramp-shaped reduction of the pressure delivered by the device as long as there is no respiratory event. The method involves repeated measurement of a flow of breath during the operation of the continuous positive airway pressure device (1) and determining at least one respiratory event from the measured time variation of the flow of breath, whereby a respiratory event represents an indication that the pressure from the continuous positive airway pressure device is too low. It involves slow, quasi-ramp-shaped reduction of the pressure delivered by the device as long as there is no respiratory event. Independent claims are also included for the following: (a) a device for carrying out continuous positive airway pressure therapy (b) and a memory medium for use with a continuous positive airway pressure device.