Quantitative feedback theory (QFT) is used to synthesize compensators, satisfying various design specifications stipulated in the benchmark problem given by B. Wie and D. S. Bernstein (Proc. Amer. Contr. Conf., pp. 961-962, May 1990). The two QFT designs satisfy all the design specifications as confirmed by computer simulations. It is shown that although by increasing controller complexity it is generally possible to reduce its bandwidth, a point can be reached where a further increase in controller complexity cannot bring about a further reduction in controller bandwidth without altering the performance specifications.