A pump supplies pressurized air to inflate compression garments, mattresses, cushions, or similar at the desired times and to desired pressures appropriate to the therapy. The garments are each identified by small steps generated in the pressure waveform during inflation, with the identifying means including a flat sheet valve in the connector chamber having vents to atmosphere and being situated along the flow path from the pump to the garment(s). As the air flows through the connection tubing and through the connector a pressure wave is generated by the valve and fed back upstream to a pressure sensor in the pump. The shape of the pressure waveform identifies a particular compression garment, the pump supplying the appropriate inflation regime upon detection of this pressure waveform.