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Many sensor network applications require consistent coverage of the region in which they are deployed over the course of the network lifetime. However, because sensor networks may be deployed randomly, node distribution and data redundancy in some regions of the network may be lower than in others. The sensors in the sparsest regions should be considered more critical to the sensor network application since their removal would likely result in unmonitored regions in the environment. For this reason, sensors in the more densely deployed regions should be considered more favorable as candidates to route the traffic of other nodes in the network. In this work, we propose several coverage-aware routing costs that allow traffic to be routed around the sparsely deployed regions so that the coverage of the environment can remain high for a long lifetime. We also propose an integrated route discovery and sensor selection protocol called DAPR that further lengthens network lifetime by jointly selecting routers and active sensors, again with the goal of minimizing the use of sensors in sparsely covered areas. Simulation results show the effectiveness of our approach in extending network lifetime nearly to the extent that can be reached using a centralized approach based on global network knowledge.