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The limited energy of sensor nodes in wireless sensor networks strongly recommends power-aware design methodologies. In this paper, a power-aware sensor selection strategy for wireless sensor networks is presented that is especially designed for distributed detection with soft decision fusion. The objective is to minimize the global probability of error at the fusion center under a total network power constraint. The cross-layer approach for the selection of a proper subset of sensors is based on a measure of individual sensor detection quality as well as location information. It corresponds to a low-complexity power allocation algorithm and enables significant performance gains in terms of reduction of the global probability of error compared to the inclusion of all sensors.