In this contribution a novel reduced-bandwidth iterative binaural MVDR beamformer is proposed. The proposed method reduces the bandwidth requirement between hearing aids to a single channel, regardless of the number of microphones. The algorithm is proven to converge to the optimal binaural MVDR in the case of a rank-1 desired source correlation matrix. Comprehensive simulations of narrow-band and speech signals demonstrate the convergence and the optimality of the algorithm.