An example method is disclosed that is implemented by a base station that supports a plurality of UEs configured to use DRX. The base station transmits respective individual scheduling assignments to each UE in a group of the UEs during an initial, on Duration portion of a DRX cycle, thereby preventing the group of UEs from immediately entering a DRX mode after the onDuration of the DRX cycle. For each UE in the group, the scheduling assignments schedule a respective first data transmission during the onDuration, and also schedule a respective second data transmission after the onDuration but within the DRX cycle. The base station transmits the scheduled first data transmissions during the onDuration of the DRX cycle, and transmits the scheduled second data transmissions after the onDuration but within the DRX cycle. For each UE in the group, its second data transmission includes more data than its first data transmission.