A comparative study of Li[LixMn2-x]O-4 and LT-LiMnO2 for lithium-ion batteries was done in order to understand anomalous behavior of the Li-Mn-O ternary phases in terms of solid-state electrochemistry. Stoichiometric LiMb(?)2O(4) shows the largest capacity at 4 V versus Li while its rechargeable capacity fades rapidly. Conversely, nonstoichiometric Li[LixMn2-x]O-4 (normally 0 < x < 1/3 in assumed defect-spinel formulation) shows excellent rechargeability compared with stoichiometric LiMn2O4 although the rechargeable capacity monotonically decreases as x in Li[LixMn2-x]O-4 increases, indicating a trade-off relation between cycleability and rechargeable capacity in applying this material to lithium-ion batteries, LT-LiMnO2 shows rechargeable capacity of more than 150 mAh g(-1) in voltages between 2.0 and 4.0 V after converting its structure to a cubic phase during the first charge. Differences and similarities between the two cubic (Li-Mn-O) phases are described and the specific problems in developing materials for lithium-ion batteries are discussed.