Embodiments herein include methods and arrangements for controlling access of mobile devices to a network, such as GSM. The mobile devices belong to an access control class (ACC) and also belong to an additional access control class (EACC) that provides extended access control. The arrangement broadcasts system information to the mobile devices that comprises a first indicator indicating an ACC. The first indicator indicates whether a mobile device is allowed to access or is barred from accessing the network. The system information further comprises a second indicator indicating an EACC. The second indicator indicates whether a mobile device is allowed to access or is limited from accessing the network. Limited access may entail blocking a mobile device from initiating communications with the network, blocking the mobile device from receiving network initiated communications, or both. A mobile device blocked from network initiated communication may not answer a page from the network.