A method has been proposed for designing an LQI servosystem in which reference characteristics and disturbance characteristics can be adjusted separately. The paper extends the method to the case in which the plant has a cascaded pure delay. It is proved that the resulting optimal compensator is the same as that for the plant with the delay removed, except for the existence of a state-prediction mechanism to cope with the delay, and that all the fundamental desirable features are inherited from the delay-free case. From the results of the paper, a complete solution to the optimal-design problem of state-predictive two-degree-of-freedom LQI servosystems for step references and step disturbances is obtained.