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Powerline communications (PLC) are currently being considered as an alternative for high-speed data communications and Internet access. With multiple outlets in almost every room, power lines are already the most pervasive network in the home or small office. This work presents a new medium access control (MAC) protocol for the "last mile" access PLC networks. Via an extensive simulation study, our protocol is compared to a well-known protocol from the literature in terms of the efficiency of the transmission of short messages; our protocol is shown to excel both in network utilization and in the average signaling delay required for the completion of the transmission request procedure, in both the cases of a lightly and heavily disturbed PLC network.