Techniques for communication over flat multi-input, multi-output (MIMO) channels are well established when either 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 explored, such information could improve system performance and reduce the demand on feedback channels or the quality of channel estimates. In this paper, a simple design scheme is introduced, that approximately maximizes the data rates of MIMO communication systems where the transmiter have access to partial channel state information in the form of covariance feedback or erroneous channel estimates. The presented algorithm is computationally attractive and gains compared with systems not exploring this information are demonstrated.