A compressor, in particular for air conditioning systems in motor vehicles, having a housing, a housing sealing cover, a drive shaft with bearings and a drive device for pistons that are displaced back and forth. The drive device transfers the rotational displacement of the drive shaft into the back-and-forth displacement of the pistons. The compressor also includes a cylinder block, in which the pistons that are displaced back and forth take in and compress coolant, a valve device, in addition to a valve plate with intake and discharge valves comprising intake and discharge chambers for an intake pressure zone and a discharge pressure zone. A cylinder head may be a separate element from the housing, in pot-shaped form, or the housing sealing cover. The intake and discharge chambers, the valve device, and the cylinder block may be situated in the closed side of the pot-shaped housing.