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In a binaural hearing aid system, output signals need to be generated for the left and the right ear. Using the binaural multichannel Wiener filter (MWF), which exploits all microphone signals from both hearing aids, a significant reduction of background noise can be achieved. However, due to power and bandwidth limitations of the binaural link, it is typically not possible to transmit all microphone signals between the hearing aids. To limit the amount of transmitted information, this paper presents reduced-bandwidth MWF-based noise reduction algorithms, where a filtered combination of the contralateral microphone signals is transmitted. A first scheme uses a signal-independent beamformer, whereas a second scheme uses the output of a monaural MWF on the contralateral microphone signals and a third scheme involves an iterative distributed MWF (DB-MWF) procedure. It is shown that in the case of a rank-1 speech correlation matrix, corresponding to a single speech source, the DB-MWF procedure converges to the binaural MWF solution. Experimental results compare the noise reduction performance of the reduced-bandwidth algorithms with respect to the benchmark binaural MWF. It is shown that the best performance of the reduced-bandwidth algorithms is obtained by the DB-MWF procedure and that the performance of the DB-MWF procedure approaches quite well the optimal performance of the binaural MWF.