A method for reducing collisions during the initial access by a plurality of mobile-terminal devices to a base station which comprises a control unit, wherein the control unit administers at least one random-access resource, wherein the method contains the following method steps: setting (S1) by the control unit of a priority which specifies which mobile-terminal device is allowed to connect to the at least one random-access resource; broadcast (S2) of the priority by the base station on at least one known channel.