Abstract: A method for controlling transmit power for connections between a base station and mobile stations of a radio communications system includes the steps of designating a direction of transmissions from mobile stations to a base station as an upward direction, and designating a direction of transmissions from the base station to the mobile stations as a downward direction. Information is transmitted to the mobile stations in the downward direction simultaneously in one frequency channel. Received powers are determined at at least two of the mobile stations. A dynamic range of transmit powers for the frequency channel is set. Transmit powers for the base station are determined. The determined transmit powers are mobile-station-specific by taking the received powers into account. A minimum transmit power is at least equal to a maximum transmit power minus the dynamic range. A device for controlling the transmit power is also provided.