Strategies for Li-ion batteries that are based on lithium-insertion compounds as cathodes are limited by the capacities of the cathode materials and by the safe charging rates for Li transport across a passivating SEI layer on a carbon-based anode. With these strategies, it is difficult to meet the commercial constraints on Li-ion batteries for plug-in-hybrid and all-electric vehicles as well as those for stationary electrical energy storage (EES) in a grid. Existing alternative strategies include a gaseous O2 electrode in a Li/air battery and a solid sulfur (S8) cathode in a Li/S battery. We compare the projected energy densities and EES efficiencies of these cells with those of a third alternative, a Li/Fe(III)/Fe(II) cell containing a redox couple in an aqueous solution as the cathode. Preliminary measurements indicate proof of concept, but implementation of this strategy requires identification of a suitable Li+-ion electrolyte.