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In this work we present a new low-power medium access scheme for sensor-type networks specifically with low traffic intensity. We call the proposed scheme DCW-MAC where ultra-low-power wake-up receivers are combined with optimal duty-cycled listening. First we introduce a framework for the analysis of energy consumption of the studied network type, then we use it to optimize the MAC scheme to achieve very low total energy consumption per transmitted data packet. It is shown that even with large sacrifices in terms of wake-up receiver detection performance, required to achieve ultra-low-power consumption with a limited form factor, we can achieve very competitive total energy consumption and outperform other MAC schemes for scenarios with low traffic.