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The strict resource-constrained conditions under which Wireless Sensor Networks (WSNs) operate impose primary restrictions on power consumption. Algorithms implemented on sensor nodes should refrain from performing complex computations in order to prolong the lifetime of the overall WSN. The IEEE 802.15.4 standard is the appropriate suite of specifications that conforms to the distinguished characteristics of WSNs. This standard is suited for low data rate, low power, and low radio transmission ranges that are typical in WSNs. This paper proposes a modification to the IEEE 802.15.4 standard that achieves efficient power savings for the sensor nodes, better channel utilization, and improved reliability. The proposal is based on the addition of a sleeping state that allows nodes to save more power while reducing the level of packet collisions. The sleeping periods can be tuned such that the highest level of channel utilization is achieved. A theoretical analysis based on Markov chain is performed to derive a mathematical model for our proposal. Using Matlab software, we show that we can achieve high levels of channel utilization, enhance reliability, and save more power compared to the performance of the original IEEE 802.15.4 standard.