In a liquid-ring rotary compressor having a control element with a suction port, a pressure orifice, and a plurality of supplementary ports in front of the pressure orifice with respect to the direction of rotation of the compressor impeller, each supplementary port having a back-pressure valve, pressure losses are reduced by decreasing the flow area of the supplementary ports toward the pressure orifice so that the total flow area for the supplementary ports that are exposed by the back-pressure valves during the compression operation is roughly proportional, with respect to the prevailing nominal pressure condition of the compressor, to the gas mass existing in the vane chambers. Embodiments for flat and conical control elements is disclosed.