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As wireless sensor networks continue to attract more attention, new ideas for applications are continually being developed, many of which involve consistent coverage of a given surveillance area. Recently, several protocols and architectures have been proposed to maintain network connectivity and adequate coverage quality while minimizing the drain on the scarce energy resources of the sensor nodes. In this paper, we propose DAPR, an integrated protocol for routing and coverage preservation that is distinctly different from the previously proposed solutions. Guided by the intuition that certain sensors are more important to the sensing application than others because of limited neighborhood redundancy, we introduce a new routing metric-an "application cost"-that aims to avoid the use of sensors in areas of critically sparse sensor deployment as routers. We have implemented DAPR in the ns-2 simulator and present simulation results showing the effectiveness of the protocol in extending network lifetime.