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 comprising • an input unit providing at least two input audio data streams (x 1, x 2), each comprising a mixture of a target signal component (s 1, s 2) from a target sound source and a noise component (v 1, v 2) from one or more noise sources; • a processor for receiving said at least two input audio data streams (x 1, x 2), and for mixing said at least two input audio data streams, or processed versions thereof, and for providing a processed input signal (y) based thereon; • an output unit providing output stimuli perceivable to the user as sound based on said processed input signal (y) or a processed version thereof; CHARACTERIZED IN THAT, • the processor is configured to estimate a noise variance (σ 1 2, σ 2 2) of each of the at least two input audio data streams (x 1, x 2) prior to mixing, to process said noise components (v 1, v 2) in dependence of the noise variances (σ 1 2, σ 2 2) of the at least two input audio data streams (x 1, x 2) to reduce or avoid artefacts in said processed input signal (y) due to said mixing by equalizing said noise components of the at least two input audio data streams (x 1, x 2) in the processed input signal (y); and • to fade from a first input audio data stream (x 1) to a second input audio data stream (x 2) among said at least two input audio data streams (x 1, x 2) over a certain fading time period, wherein said fading comprises determining respective fading parameters or a fading curve that gradually decreases a weight (α) of said first input audio data stream (x 1), or a processed version thereof, while increasing a weight (1 - α) of said second input audio data stream (x 2), or a processed version thereof, and wherein the perceived noise level of the processed input signal (y) is substantially unaltered during said fading by ensuring that the noise components (v 1, v 2) in the processed input signal (y) are equalized to the level of the noise signal components in the input audio data stream exhibiting the largest noise level, by adding additional noise (v 3) to the processed input signal (y), wherein the variance (σ 3 2) of the additional noise (v 3) is adapted depending on the estimated noise variances (σ 1 2, σ 2 2) and the weight α. • an input unit providing at least two input audio data streams (x 1, x 2), each comprising a mixture of a target signal component (s 1, s 2) from a target sound source and a noise component (v 1, v 2) from one or more noise sources; • a processor for receiving said at least two input audio data streams (x 1, x 2), and for mixing said at least two input audio data streams, or processed versions thereof, and for providing a processed input signal (y) based thereon; • an output unit providing output stimuli perceivable to the user as sound based on said processed input signal (y) or a processed version thereof; CHARACTERIZED IN THAT, • the processor is configured to estimate a noise variance (σ 1 2, σ 2 2) of each of the at least two input audio data streams (x 1, x 2) prior to mixing, to process said noise components (v 1, v 2) in dependence of the noise variances (σ 1 2, σ 2 2) of the at least two input audio data streams (x 1, x 2) to reduce or avoid artefacts in said processed input signal (y) due to said mixing by equalizing said noise components of the at least two input audio data streams (x 1, x 2) in the processed input signal (y); and • to fade from a first input audio data stream (x 1) to a second input audio data stream (x 2) among said at least two input audio data streams (x 1, x 2) over a certain fading time period, wherein said fading comprises determining respective fading parameters or a fading curve that gradually decreases a weight (α) of said first input audio data stream (x 1), or a processed version thereof, while increasing a weight (1 - α) of said second input audio data stream (x 2), or a processed version thereof, and wherein the perceived noise level of the processed input signal (y) is substantially unaltered during said fading by ensuring that the noise components (v 1, v 2) in the processed input signal (y) are equalized to the level of the noise signal components in the input audio data stream exhibiting the largest noise level, by adding additional noise (v 3) to the processed input signal (y), wherein the variance (σ 3 2) of the additional noise (v 3) is adapted depending on the estimated noise variances (σ 1 2, σ 2 2) and the weight α.