The Long Term Evolution (LTE) standard specifies the Discontinuous Reception Mechanism (DRX) mechanism for saving power at the User Equipment (UE). Here, a UE switches off its RF circuitry when there are no packets to be transmitted or received. The existing DRX algorithms use static operational parameters that are determined by the evolved nodeB (eNB) at the start of a UE's session. During the switch-off period, packets destined to the UE are buffered in the eNB leading to higher packet latency. This paper presents two adaptive algorithms to dynamically adjust the DRX parameters, in order to reduce both energy consumption and the extra delay incurred. The algorithms use application Quality-of-Service (QoS) and Channel Quality Information (CQI) to adjust the DRX parameters. Performance studies based on ns3 simulator show that the algorithms are able to reduce packet delay compared to static DRX by up to 60%, 60% and 75% and reduce energy consumption by up to 75%, 43% and 90% for video streaming, VoIP and bursty data applications respectively.