A private radio system within a serving cell of a cellular communications system periodically monitors the broadcast information transmitted on the control channels of the serving and surrounding cells. From this monitoring, all those carrier frequencies serving as control channels are derived for the cell areas around the serving cell and a control channel list constructed. The private radio system then carries out signal strength measurements on the downlink control channels, and orders the control channel list accordingly. Alternatively, a mobile station that is attached to a private radio system can perform the downlink measurements and forward the measurements to the private radio system. In either event, the private radio system selects a communication channel from the ordered list and derives, from the received signal strength values of the control channels, the transmit power level required to both overcome interference caused by more distant cellular base stations and, at the same time, not interfere with those stations.