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Geographic routing is a useful and scalable point-to-point communication primitive for wireless sensor networks. However, previous work on geographic routing makes the unrealistic assumption that all the nodes in the network are awake during routing. This overlooks the common deployment scenario where sensor nodes are duty-cycled to save energy. In this paper we investigate several important aspects of geographic routing over duty-cycled nodes. First, we extend existing geographic routing algorithms to handle the highly dynamic networks resulting from duty-cycling. Second, we provide the first formal analysis of the performance of geographic routing on duty-cycled nodes. Third, we use this analysis to develop an efficient decentralized sleep scheduling algorithm for reducing the number of awake nodes while maintaining both network coverage and a (tunable) target routing latency. Finally, we evaluate via simulation the performance of our approach versus running existing geographic routing algorithms on sensors duty-cycled according to previous sleep scheduling algorithms. Our results show, perhaps surprisingly, that a network of duty-cycled nodes can have slightly better routing performance than a static network that uses comparable energy. Our results further show that, compared to previous algorithms, our sleep scheduling algorithm significantly improves routing latency and network lifetime.