NOVELTY - Electrolyte comprises a lithium salt, and a non-aqueous organic solvent comprising a 1H-pyrrole or thiophene compound (I), where (I) is included at greater than or equal to 0.001 vol.% to less than 1 vol.% based on the total volume of the non-aqueous organic solvent.    USE - The electrolyte is useful in a rechargeable lithium battery (claimed).    ADVANTAGE - The electrolyte provides the rechargeable lithium battery with improved cycle-life characteristics, storage characteristics, and/or stability.    DETAILED DESCRIPTION - Electrolyte comprises a lithium salt, and a non-aqueous organic solvent comprising a 1H-pyrrole or thiophene compound of formula (I), where (I) is included at greater than or equal to 0.001 vol.% to less than 1 vol.% based on the total volume of the non-aqueous organic solvent. The electrolyte does not include a halogen (X') of the form X'2 or H-X'.    X = N or S;    R1, R2 = 1-30C alkyl, 3-30C cycloalkyl, 6-30C aryl, 2-30C alkenyl, 3-30C cycloalkenyl, 2-30C alkynyl, 3-30C cycloalkynyl, 2-30C heterocycloalkyl, 2-30C heteroaryl, 1-30C alkoxy (all optionally substituted), H, halo, CN, NO2, or aldehyde;    R = 1-30C alkyl, 3-30C cycloalkyl, 6-30C aryl, 7-20C arylalkyl, 2-30C alkenyl, 3-30C cycloalkenyl, 2-30C alkynyl, 1-20C heteroalkyl, 2-30C heterocycloalkyl, 2-30C heteroaryl (all optionally substituted), -SiR33, -NR4R5, or -PR6R7; and    R3-R7 = 1-30C alkyl, 3-30C cycloalkyl, 2-30C alkenyl, or 6-30C aryl (all optionally substituted).    INDEPENDNET CLAIMS are included for:    (1) a rechargeable lithium battery (3) comprising a positive electrode (5) comprising a positive active material, a negative electrode (6) comprising a negative active material, and the electrolyte; and    (2) fabricating the rechargeable lithium battery, comprising obtaining a positive electrode comprising a positive active material and a negative electrode comprising a negative active material, obtaining the electrolyte, and impregnating the electrolyte into the positive electrode and the negative electrode.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a rechargeable lithium battery.    Rechargeable lithium battery (3)    Electrode assembly (4)    Positive electrode (5)    Negative electrode (6)    Separator. (7)