A compressor, particularly suited for use in the motor vehicle air conditioning system, having a compact and simple design. The housing is constructed of a body portion having a first wall area which defines the cavity containing the pumping unit and is designed to withstand the internal cavity pressure. A second wall area, not designed to withstand the internal cavity pressure, cooperates with a housing cover to seal the housing. The second wall area is under tension and is attached to the body by welding or by bending the second wall area. The cover includes a pair of pressure cavities separated by concentric annular sealing bridges. The sealing bridges have axially offset sealing surfaces which cooperate with a valve plate to seal off the two chambers. The sealing surface of the radially outer bridge may be formed of any elastic material. A drive-shaft and swash plate cooperate with a take-up plate to operate one or more pistons. A drive plate, integral with, or attached, as by welding, etc. to the compressor drive-shaft, is coupled to the swash plate. A projecting portion of the take-up plate having a first bearing surface is slidably connected to a support element.