A hearing assistance system, comprising a first hearing device to be worn at a first one of a user's ears, a second hearing device to be worn at a second one of the user's ears, and an external audio source device for transmitting an external audio data stream, each hearing device comprising an interface for wireless data exchange with the external audio source device, including receipt of the external audio data stream from the external audio source device, and at least one microphone for capturing an audio signal from a user's voice, each hearing device being adapted to transmit such microphone audio signal via the interface to the external audio source device, the hearing devices being adapted to establish a binaural link between the first hearing device and the second hearing device, the hearing assistance system being adapted to estimate at least one of a quality of links (30, 31) from the external audio source device to the hearing devices by monitoring at least one parameter indicative of the link quality, a battery charge state of each of the hearing devices by repeatedly measuring the battery voltage and an audio signal quality of the microphone audio signal of each hearing device by determining the SNR of the respective microphone audio signal and to communicate such link quality estimation, battery charge state estimation and the audio signal quality estimation, respectively, at least to the two hearing devices; characterized by the hearing assistance system being adapted to decide, based on such link quality estimation, battery charge state estimation and/or audio signal quality estimation, respectively, whether none of the hearing devices, one of the hearing devices or each hearing device is to transmit its microphone audio signal via its interface to the external audio source device. each hearing device comprising an interface for wireless data exchange with the external audio source device, including receipt of the external audio data stream from the external audio source device, and at least one microphone for capturing an audio signal from a user's voice, each hearing device being adapted to transmit such microphone audio signal via the interface to the external audio source device, the hearing devices being adapted to establish a binaural link between the first hearing device and the second hearing device, the hearing assistance system being adapted to estimate at least one of a quality of links (30, 31) from the external audio source device to the hearing devices by monitoring at least one parameter indicative of the link quality, a battery charge state of each of the hearing devices by repeatedly measuring the battery voltage and an audio signal quality of the microphone audio signal of each hearing device by determining the SNR of the respective microphone audio signal and to communicate such link quality estimation, battery charge state estimation and the audio signal quality estimation, respectively, at least to the two hearing devices; characterized by the hearing assistance system being adapted to decide, based on such link quality estimation, battery charge state estimation and/or audio signal quality estimation, respectively, whether none of the hearing devices, one of the hearing devices or each hearing device is to transmit its microphone audio signal via its interface to the external audio source device.