Techniques are described herein that enhance the following: (1) how a wireless device conveys a change of its downlink (DL) coverage class (CC) to a network; and (2) how the network and the wireless device each perform a new paging group procedure to align coverage class paging groups within a given Extended Discontinuous Receive (eDRX) cycle for the wireless device. In addition, devices namely a wireless device, a radio access network node (e.g., Base Station Subsystem), and a core network node (e.g., Serving GPRS Support Node) that implement these techniques are described herein.