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Even self-deployment is one of the best strategies to deploy mobile sensors when the region of interest is unknown and manual deployment is infeasible. A widely used distributed algorithm, Lloyd`s method, can achieve even self-deployment. It however suffers from two critical issues when being used in mobile sensor networks. First, it does not consider limited sensor communication range. Second, it does not optimize sensor movement distances, and hence can lead to excessive energy consumption, a primary concern in sensor networks. This paper first formulates a locational optimization problem that achieves even deployment while it takes account of energy consumption due to sensor movement, and then proposes two iterative algorithms. The first algorithm, named Lloyd- α, reduces the movement step sizes in Lloyd`s method. It saves traveling distance while maintaining the convergence property. However, it leads to a larger number of deployment steps. The second algorithm, named Distributed Energy-Efficient self-Deployment (DEED), reduces sensor traveling distances and requires a comparable number of deployment steps as that in Lloyd`s method. This paper further proposes an intuitive method to deal with limited sensor communication range that is applicable to all three methods. Extensive simulation using NS-2 demonstrates that DEED leads to up to 54 percent less traveling distance and 46 percent less energy consumption than Lloyd`s method.