Optimal H??-controllers may exhibit large gains, resulting in large control efforts. In this paper we consider the problem of designing a minimum gain static full state-feedback controller such that the closed-loop transfer function satisfies a H??-constraint. The main result of the paper shows that, by minimizing an upper bound for the Frobenius-norm of the feedback-gain matrix and using a parametrization as in [6], the problem can be cast into a finite-dimensional, convex optimization problem. Scalar cost-functions for the H??-bound and various other constraints allow the application of gradient-based software packages to these problems. Finally, we illustrate how to apply this theory to the mixed H2/H??-control problem with minimum control effort.