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The question of improving efficiencies of operation is nowadays more than ever considered a very critical issue. This is because losses have acquired recently an extra cost that of the CO2 release penalty. It is well known that a good portion of the electricity required to operate a power grid is spent as Overhead Line (OHL) power losses. In this paper the key points of the theory of maximum OHL transmission efficiency are reviewed. The OHL loading corresponding to the maximum transmission efficiency is given. Then by means of a case study it is shown how to optimize the transmission efficiency of double-circuit overhead lines for the periods of off-peak loading of the lines. The transmission efficiency vs. line loading curves of the OHL are presented and the change of character from capacitive to inductive with increasing load of the OHL is illustrated. The potential gains in percentage points of the transmission efficiency are calculated. Conclusions of practical importance are drawn both for line design purposes as well as for the line operation optimization.