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Deterministic deployment of distributed sensor networks (DSNs) is sometimes impractical in situations where a global map of the environment is either unavailable or of little use because the environment is dynamic or hostile. One way to deal with such situations is to randomly scatter sensor nodes in the area of interest. However, the deployment carried out in such a way is generally far from optimal and the resulting uneven node topology can lead to poor utilization of the available sensors and a short network lifetime. This paper proposes an energy-efficient self-organizing technique based on fuzzy logic systems (FLSs) for enhancing the coverage of a DSN after an initial random placement of sensors. Fuzzy logic has been applied previously to the deployment of DSNs and was successful to overcome most of the limitations of other algorithms. However, sensor's present remaining energy level was not considered in decision making and therefore the method was not very power-aware. Since the self-deployment process is very energy consuming and energy is the main operating constraint, it is necessary to utilize the limited energy of each sensor in a relatively fair fashion. Simulation results show that our approach not only achieves a fast and stable deployment that maximizes coverage but also optimizes the overall energy consumption during deployment, thereby prolonging the lifespan of the network.