The invention relates to electronic integrated circuits capable of operating either in active mode or in standby mode and to have, in standby mode, a very low current consumption. According to the invention, the leakage current of a power transistor inserted in series between a supply terminal and an active circuit is controlled by a gate reverse overbias in the following manner: a first reference transistor, and a second reference transistor identical to the first, are biased with the same gate reverse overbias voltage as the power transistor, the first transistor having its source linked to the supply terminal, and the second reference transistor having its source linked to its drain. The leakage currents in these two transistors are compared, and it is considered that the optimal bias of the gate is obtained when the leakage currents are equal. Applications to circuits supplied by a battery or a cell (portable telephones, cameras, portable computers, etc.).