Abstract: A piston pump with at least one driven stepped piston element disposed longitudinally movably in a housing is disclosed. The piston element and housing define a plurality of pressure chambers whose volumes vary as a function of the motion of the stepped piston. A volume of the first pressure chamber is decreased during an intake stroke of the piston that increases the volume of the second pressure chamber. A volume of a third pressure chamber, communicating with the pumping side and defined by the stepped piston element and the housing, is increased by a defined volumetric value during the compression stroke and decreased by the during the intake stroke; the defined volumetric value is less than the change in volume of the second pressure chamber during the compression stroke of the stepped piston element.