A rechargeable lithium-sulfur cell comprising a cathode, an anode, a separator electronically separating the two electrodes, a first electrolyte in contact with the cathode, and a second electrolyte in contact with the anode, wherein the first electrolyte contains a first concentration, C1, of a first lithium salt dissolved in a first solvent when the first electrolyte is brought in contact with the cathode, and the second electrolyte contains a second concentration, C2, of a second lithium salt dissolved in a second solvent when the second electrolyte is brought in contact with the anode, wherein C1 is less than C2. The cell exhibits an exceptionally high specific energy and a long cycle life.