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Idle-listening is the biggest challenge for energy-efficiency and longevity of multihop wireless sensor network (WSN) deployments. While existing coordinated sleep/wakeup scheduling protocols eliminate idle-listening for simple traffic patterns, they are unsuitable to handle the complex traffic patterns of the random routing protocols. We present a novel coordinated sleep/wakeup protocol PowerNap, which avoids the overhead of distributing complex, large sleep/wakeup scheduling information to the nodes. PowerNap piggybacks onto the relayed data packets the seed of the pseudo-random generator that encodes the scheduling information, and enables any recipient/snooper to calculate its sleep/wakeup schedule from this seed. In essence, PowerNap trades off doing extra computation in order to avoid expensive control packet transmissions. We show through simulations and real implementation on TelosB motes that PowerNap eliminates the idle-listening problem efficiently and achieves self-stabilizing, low-latency, and low-cost relaying of data packets for random routing protocols.