A high performance lithium-sulfur battery cell (10) includes the following features: (a) a negative electrode (14) including a metal or an ion of the metal; (b) a positive electrode (18) comprising an electronically conductive material; and (c) a liquid catholyte (16) including a solvent and a dissolved electrochemically active material comprising sulfur in the form of a sulfide of the negative electrode metal or a polysulfide of the metal. Such battery cells are characterized by an energy density, calculated based upon a laminate weight, of at least 400 Watt-hours/kilogram when discharged at a rate of at least 0.1 mA/cm2. Cells meeting these criteria often find use as primary cells.