A hearing device, e.g. a hearing aid, adapted for being located at or in an ear, or to be fully or partially implanted in the head, of a user, the hearing device comprises a) an input unit providing at least two input audio data streams, each comprising a mixture of a target signal component from a target sound source and a noise component from one or more noise sources; b) a mixing processor for receiving said at least two input audio data streams, and for mixing said at least two input audio data streams, or processed versions thereof, and for providing a processed input signal based thereon; c) an output unit providing output stimuli perceivable to the user as sound based on said processed input signal or a processed version thereof. The processor is configured to process said noise component of said at least two input audio data streams, or processed versions thereof in order to reduce or avoid artefacts in said processed input signal due to said mixing. A method of operating a hearing device is further disclosed. The invention may e.g. be used in hearing aids, e.g. hearing aids configured to communicate with another device, e.g. binaural hearing aid systems.