A systematic, rapidly converging process for achieving the best fit to a set of phase shifts by means of a phenomenological potential of a given analytic form is described. The discussion is limited, in the main, to the case of central forces. A corrector formula is given for the simultaneous adjustment of the parameters of the potential. As an example of its efficiency we present the results obtained after a small number of iterations in trying to fit the $p$-wave phase shifts of elastic proton-alpha scattering at low energy.