It is well understood that the maximum likelihood estimator is a powerful equalisation technique for frequency selective fading channels, and in particular for MIMO systems. The complexity of this estimator, however, grows exponentially with the number of users and multipath taps, hence limiting the use of this algorithm in MIMO systems. In the paper, the authors propose a joint spatial and temporal channel-shortening filter as a pre-processor to reduce significantly the complexity of a maximum likelihood estimator. Their design is based on both minimum mean square error and maximum signal-to-noise ratio criteria. They compare the performance of their proposed schemes with the existing methods that employ channel-shortening techniques only in the spatial or temporal dimension, and thereby demonstrate the advantage of using joint spatial and temporal channel shortening in terms of complexity and bit error rate performance.