The cost of electrodialysis (ED) systems can be decreased by decreasing their power consumption. Such reductions may be achieved by using degrees of freedom in the system's configuration to obtain a more uniform spatial distribution of the rate of entropy generation, as explained by the theorem of equipartition of entropy generation. In this paper, we study possible improvements to the energy efficiency of electrodialysis through the use of two electric stages with different voltages, and through operation in a counterflow configuration. We first consider how a two-stage ED system should be operated. In particular, we look at how the voltages and current densities should be chosen. In addition, we quantify the effect of operating under two voltages in brackish-water desalination and in high-salinity brine concentration. Finally, we quantify the effect of operating ED in counterflow for the same applications. We show that high ED fixed costs prevent the achievement of significant improvements in energy efficiency. If fixed costs are reduced, and larger systems become cost-effective, we show that a power reduction of up to 29% is possible by going from a single-stage to a two-stage configuration.