A lithium-sulfur battery is disclosed in one embodiment of the invention as including an anode containing lithium and a cathode comprising elemental sulfur. The cathode may include at least one solvent selected to at least partially dissolve the elemental sulfur and Li2Sx. A substantially non-porous lithium-ion-conductive membrane is provided between the anode and the cathode to keep sulfur or other reactive species from migrating therebetween. In certain embodiments, the lithium-sulfur battery may include a separator between the anode and the non-porous lithium-ion-conductive membrane. This separator may prevent the lithium in the anode from reacting with the non-porous lithium-ion-conductive membrane. In certain embodiments, the separator is a porous separator infiltrated with a lithium-ion-conductive electrolyte.