This invention is a multi-stage compressor (1,5) embodying a stepped piston (5) in a stepped cylinder (1) and con­ nected through a coaxial rod (4) to the piston (3) of an engine. Control means (10) in a passageway or a conduit extending from the second (5e) or third stage (5f) discharge of the compressor or any other source of pressure to a single bounce chamber (9), responds to pressure in the bounce chamber (9) to increase or reduce gas pressure in the chamber, to balance the energy and work quantities acting in opposite directions to provide optimum operation of the compressor (1,5) at var­ ying pressures.