LTE and LTE-Advanced mobile technologies have integrated discontinuous reception (DRX) power saving method to optimize the power consumption at the user equipment (UE). The DRX method was proposed by the 3rd Generation partnership Project (3GPP), and since then, the traffic behavior has been analyzed in several studies with a standard 3-state DRX model to describe the trade-off between power saving and delay. In this paper, we presented a novel 4-state and 5-state 3GPP LTE DRX mechanisms. The proposed mechanisms were developed by augmenting (an) active state(s) to deep and/or light sleep cycle of standard 3-state DRX for handling a small burst of packets, thereby bypassing the process of returning to the timer-dependent active mode. We have generated analytical models using a semi-Markov process for bursty packet data traffic and evaluated these augmented DRX mechanisms against a standard 3-state DRX method. Overall, the analytical results from varying timing parameters showed that our augmented DRX (both 4-state and 5-state) improved power saving factor (ranging between 1% and 8%) and reduced delay (ranging between 20% and 60%) compared to the standard 3-state DRX. Furthermore, the magnitude of improvement for both delay and power-saving was somewhat greater in 5-state than 4-state.