This paper proposes a fixed-structure technique for synthesizing controllers that are optimal with respect to various operator norms. An optimal control problem is developed for each of these operator norms, and necessary conditions for sub-optimal performance are derived. Mixed-norm optimal control problems are also formulated. A continuation algorithm using quasi-Newton corrections is used to compute approximate solutions of the necessary conditions for a sequence of problems whose solutions approach an optimal controller. Optimal controllers with respect to each of the operator norms are synthesized for a 4th-order mass-spring-dashpot system.