TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The non-aqueous electrolyte comprises a thiophene in 0.01-10, preferably 2-5 vol.%.Preferred Component: The cathode comprises transition metal chalcogenides or mixed oxide(s) of lithium and transition metal(s) and/or main group metals. The electrolyte comprises solvent(s) from esters of carbonic acid, esters or nitriles of carboxylic acids, lactones, ethers, alkanes, or perfluorinated alkanes, and conductive salt(s) from lithium salts of perfluorinated carboxylic acids and perfluorinated alkanesulfonic or arylsulfonic acids, lithium-bisfluoroalkylsulfonyl-imides, lithium-trisfluoro-alkylsulfonylmethides, lithium fluoroalkyl-phosphates, or lithium bis(oxalato)borates. It may comprise as a solvent, ethylene carbonate, propylene carbonate, diethyl carbonate, dimethyl carbonate, ethyl methyl carbonate, vinylene carbonate, or a mixture of at least two of these carbonic esters.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Component: The anode comprises metallic lithium, alloys containing metallic lithium, carbon-like optionally graphitic or non-graphitic materials, carbon-based materials containing nonmetallic components in addition to carbon, ternary compounds of boron, carbon, and nitrogen, or oxides or sulfides of main group and subgroup elements. The cathode comprises LiNi1-xCoxO2, LiNi1-x-y CoxAlyO2, LiNi1-x-zCoxMnzO2, or mixtures of these with one another or mixtures of these with other mixed oxides of lithium with transition metals and/or main group metals. The electrolyte comprises conductive salt(s) from lithium boron perfluoride, lithium phosphorus hexafluoride, lithium arsenic hexafluoride, or lithium chlorate.x = 0.05-0.5;y = 0-0.3;z = 0-0.5.    TECHNOLOGY FOCUS - POLYMERS - Preferred Component: The separator is a porous polymer. The electrolyte comprises conductive salt(s) from lithium bis((salicylato)borates) optionally embedded in a polymeric gel matrix.    TECHNOLOGY FOCUS - CERAMICS AND GLASS - Preferred Component: The separator is porous glass.    TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Property: The battery has a maximum permissible cell voltage of at least4 V. Preferred Definitions:    R1-R4 = H (preferably), 1-6C (fluoro)alkyl, 1-6C (fluoro)alkoxy, F, Cl, or CN.    At least one of the radicals R1-R4 is CN.    EXAMPLE - A cell was assembled by pushing a steel cylinder into an orifice of the housing and locking it with a screw union and a sealing ring. A cathode film was inserted and covered with a glass wool separator. The cylinder with the lithium anode was introduced through the opposite orifice of the housing and pushed up to the separator. A 1 ml electrolyte with electrolyte additive (5 vol.% thiophene-3-carbonitrile) was introduced and the separator was rendered gas-free. The anode steel cylinder was screwed tight. The cell was charged at C/15 to 4.3 V, recharged at 4.3 V to 0.04 C, and discharged again at C/15. The reversibility was 92.7% in the first cycle.