This paper introduces a nonparametric frequency-domain scheme for tuning closed-loop systems. A linear quadratic criterion is used for guiding the system towards an optimal-regulation state. The computation of tuning directions is performed with unbiased estimates of first and second derivatives of the cost function. In order to provide cautious adjustments of the controller parameters, this scheme introduces a mechanism that guarantees stability of the loop during the tuning procedure. This mechanism uses the generalised stability margin and a metric on transfer functions to impose safe limits on the variation of the control law.