A general method is described for optimizing the groove profiles of perfectly conducting gratings. The functional derivatives of the coefficients of the diffracted far field are first introduced, and it is shown that these derivatives provide all the necessary information on the ‘local’ relationship between the far field and the groove profile. The principle of several well-known minimization algorithms is recalled, and numerical examples are given which show the versatility and the efficiency of the method. Numerous extensions of the method seem to be straightforward, especially for gratings of finite conductivity.