A tensioner for a start-stop accessory drive comprises a movable support, a pulley carried by the support to contact a belt of the drive, a spring to load the support so as to tension the belt, and an actuator controlled and movable to push said pulley against the belt in one direction by means of a load in parallel and additional with respect to that of the spring and an irreversible device which enables the action of the actuator and prevents a displacement of said support in response to the loads of the belt.