The use of the ground as the current return path often presents planning and operational challenges in power distribution networks. This study presents optimization-based models for the optimal selection of conductor sizes in Single Wire Earth Return (SWER) power distribution networks. By using mixed integer non-linear programming (MINLP), models are developed for both branch-wise and primary-lateral feeder selections from a discrete set of overhead conductor sizes. The models are based on a mathematical formulation of the SWER line, where the objective function is to minimize fixed and variable costs subject to constraints specific to SWER power flow. Load growth over different time periods is considered. The practical application is tested using a case study extracted from an existing SWER distribution line in Namibia. The results were consistent for different network operating scenarios.