A key assumption made in this paper is that electric vehicle (EV) battery charging profiles are rectangular. This requires a specific and new formulation of the charging problem, involving discrete action sets for the EVs in particular. The considered cost function comprises of three components: the distribution transformer aging, the distribution energy losses, and a component inherent to the EV itself (e.g., the battery charging monetary cost). Charging start times are determined by the proposed distributed algorithm, whose analysis is conducted by using game-theoretic tools such as ordinal potential games. Convergence of the proposed algorithm is shown to be guaranteed for some important special cases. Remarkably, the performance loss w.r.t. the centralized solution is shown to be small. Simulations, based on realistic public data, allow one to gain further insights on the issues of convergence and optimality loss and provide clear messages about the tradeoff associated with the presence of the three components in the considered cost function. While simulations show that the proposed charging policy performs quite similarly to existing (continuous) charging policies such as valley-filling-type solutions when the non-EV demand forecast is perfect, they reveal an additional asset of rectangular profiles in presence of forecasting errors.