A wireless binaural hearing device system comprising: a first and a second hearing device for placement at and/or in a user's first and second ear, respectively, each hearing device comprising an output transducer for providing an output to the user, a wireless communication unit and an antenna adapted for providing a wireless link between the first and the second hearing devices (10R; 10L), an amplifier configured for amplifying signals received via the wireless link according to a gain level, and a power supply having a primary voltage source and a secondary voltage source , wherein the secondary voltage source provides a lower voltage than the primary voltage source ; and a detector arrangement adapted for determining a quality indicator indicative of the quality of the wireless link ; a control arrangement adapted to: • switch to a low power mode when the quality indicator is above a threshold, in which a transmitting hearing device of the first and second hearing devices uses its secondary voltage source to drive transmission with its antenna , and synchronously increase the gain level of a receiving device of the first and second hearing devices , and • switch to a regular power mode when the quality indicator is below the threshold, in which regular power mode the transmitting hearing device uses its primary voltage source to drive transmission with its antenna , and preferably synchronously decrease the gain level of the receiving device. a first and a second hearing device for placement at and/or in a user's first and second ear, respectively, each hearing device comprising an output transducer for providing an output to the user, a wireless communication unit and an antenna adapted for providing a wireless link between the first and the second hearing devices (10R; 10L), an amplifier configured for amplifying signals received via the wireless link according to a gain level, and a power supply having a primary voltage source and a secondary voltage source , wherein the secondary voltage source provides a lower voltage than the primary voltage source ; and a detector arrangement adapted for determining a quality indicator indicative of the quality of the wireless link ; a control arrangement adapted to: • switch to a low power mode when the quality indicator is above a threshold, in which a transmitting hearing device of the first and second hearing devices uses its secondary voltage source to drive transmission with its antenna , and synchronously increase the gain level of a receiving device of the first and second hearing devices , and • switch to a regular power mode when the quality indicator is below the threshold, in which regular power mode the transmitting hearing device uses its primary voltage source to drive transmission with its antenna , and preferably synchronously decrease the gain level of the receiving device. • switch to a low power mode when the quality indicator is above a threshold, in which a transmitting hearing device of the first and second hearing devices uses its secondary voltage source to drive transmission with its antenna , and synchronously increase the gain level of a receiving device of the first and second hearing devices , and • switch to a regular power mode when the quality indicator is below the threshold, in which regular power mode the transmitting hearing device uses its primary voltage source to drive transmission with its antenna , and preferably synchronously decrease the gain level of the receiving device. <EOS>