Many design problems, e.g. in control theory, amount to tuning a parameter vector c so as to guarantee that specifications are met for all feasible values of some unknown perturbation vector p. A new prototype algorithm for solving this guaranteed-tuning problem is proposed, and its convergence properties are established. It applies when the design specifications translate into a finite number of (possibly nonlinear) inequalities. Three test cases taken from the field of control are considered, namely the design of a PID controller robust to structured uncertainty, the control of a nonlinear discrete-time model with uncertain parameters and initial state, and a problem of motion planning, with obstacles to be avoided.