In the Long Term Evolution system Discontinuous Transmission and Reception (DRX/DTX) has been introduced to extend the terminal battery lifetime. In this paper, we study the energy-saving provided by this mechanism and the impact on the QoS performance of Voice over IP (VoIP) traffic under dynamic and semi persistent packet scheduling strategies. Simulations and analytical results show that the DRX/DTX scheme can reduce the terminal power consumption without compromising the required VoIP QoS in terms of maximum air-interface delay. However, it does not provide any further power savings if the terminal is asleep for a period longer than 20 ms. It is shown that the power savings are larger for semi persistent scheduling than for dynamic packet scheduling at the cost of a lower spectral efficiency.