For single-user, multiple-input multiple-output (MIMO) channels with Rayleigh fading correlated at the transmitter side, and where the receiver only has partial channel knowledge in form of an MMSE channel estimate, we study the joint optimization of the linear precoder and the pilot (training) sequence under the constraint of prescribed transmit power and training energy budgets. Although this joint problem is generally not convex itself, we can show that the two marginal problems of optimizing either the pilot sequence or the precoder when the other variable is fixed, are convex. Furthermore, we characterize the jointly optimal transmit and training directions. Finally, we propose a full characterization of the Pareto efficient joint power loading strategies for the case of two transmit antennas, and illustrate the behavior of the jointly optimal solution.