Signal estimation in MIMO communications typically suffers from performance degradations due to imperfect channel state information (CSI). Traditional robustification schemes rely on assumptions about the model uncertainty and may result in conservative performance. We introduce a rank-reduction approach that enhances the performance in training-based applications. A sequence of reduced-rank channel estimates are established from the training data. Multiple, distinct estimates of the transmit signal are then generated by applying standard detectors to each of those models, among which the 'best' is chosen by data-driven methods. This way significant performance improvements can be achieved, especially for ill-conditioned channels.