The problem of optimizing the training signal for the estimation of multiple-input multiple-output (MIMO) fading channels has been of a great interest in the last few years, due to its central role in combining accuracy in estimation with bandwidth efficiency. The general case of correlated channels and colored interference was recently addressed . It was shown that the optimal training for the Linear Minimum Mean Squared Error (LMMSE) estimator, in the sense of minimizing the channel estimation MSE subject to a constraint on the total transmit power, consists of a joint water-filling along the eigenmodes of the desired channel and interference covariance matrices. Thus, the resulting scheme relies on the assumption of the availability of these matrices at the transmitter, which is, in practice, realized via a feedback path. In this paper, that scheme is revisited, with the aim of reducing its requirements for side information and transmit beamforming as well as exploring efficient ways of achieving improvements on its performance. Inspired by an interpretation of the LMMSE estimator as a two-step procedure, we investigate possible gains (and tradeoffs) from an alternative scheme, in which the processing of the received data is performed on both of its dimensions, temporal and spatial. The simulation results demonstrate that this approach provides a good trade-off between estimation performance and low feedback communication and beamforming overheads.