The main contribution of this paper is a constructive parameterization of the class of almost smooth universal formulas which render a system asymptotically stable with respect to a known control Lyapunov function (CLF), and a constructive parameterization of a class of inverse optimal universal formulas having Kalman-like stability margins. The novelty of the parameterization is that it is given in terms of two function which are constrained to be locally Lipschitz and satisfy convex constraints. The implication of this result is that the CLF/universal formula approach can be combined with a priori performance objectives to design high performance control strategies. Two examples illustrate the approach.