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A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be addressed using either H, or 11 robust control theory, depending upon the uncertainty characterisation. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency domain constraints. In this paper we a d b these problems using a mixed h / H , approach. This approach allom for minimising the worst-case peak output due to a persistent disturbance, while, at the name time, satisfying an '&-norm constraint upon some closed-loop transfer function of interest. The main result of the paper shows that mixed 11/7im optimal controllers can be obtained by solving a sequence of problems, each one consisting of a finitedimensional convex optimisation and a standard, unconstrained H, problem.