In linear control system design, it is often assumed that control is unbounded. However, due to practical constraints, actuator saturation often occurs. To compensate for the actuator saturation, heuristic techniques are developed and can be found in the literature. In this paper, the optimal compensation for a class of sub-optimal control laws such as the minimum variance, generalized minimum variance,k-incremental, integrating and generalized predictive control is derived. Comparisons with non-optimal schemes such as those derived heuristically are made. It is shown that the optimal compensation scheme also yields the lowest accumulated sum of the cost function under certain conditions, although the result does not generally hold, as illustrated by a numerical example.