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Power consumption is a critical concern in communications over wireless sensor networks (WSN). In this paper, we address the rate-allocation problem for Slepian-Wolf coding of multiple correlated sources. The goal is to find the optimal rate-point that allows lossless reconstruction of the sources, while minimizing the overall transmission power consumption of the WSN under an exponential cost model. A novel water-filling algorithm to be performed by the receiver is proposed to solve the problem in a recursive manner. The feasibility and optimality of the proposed solution are analyzed mathematically and verified experimentally. Compared to the conventional Lagrangian-multiplier approach, our algorithm achieves dramatic reduction in computational complexity.