In a cellular radio system (30) the terminals (35) are arranged to set up and maintain radio communication with the base stations (31, 32, 33, 34) in the cells (31a, 32a, 33a, 34a). Regarding the setting up and maintaining of radio communication at least one terminal (35) is arranged to favor at least one cell (32a, 33a) with respect to other cells (31a, 34a), in a manner independent of other terminals. The priority data relating to a terminal are stored in a central database (37), from which they are transmitted to the terminal when it registers.