Transmission schemes for flat multi-input, multi-output (MIMO) channels are well established for the cases where perfect channel state information or no channel state information is available at the transmitter. However, communication over channels where the transmitter has access to partial or imperfect information has received less attention. If exploited, such information has the potential of improving system performance and reducing the bandwidth requirements of feedback links or the required quality of channel estimates. Herein, a simple design scheme is introduced, that approximately maximizes the data rates of MIMO communication systems where the transmitter has access to partial channel state information in the form of covariance feedback or erroneous channel estimates. An algorithm is presented which is computationally attractive and performance gains are shown when compared to systems not using this information.