Optimum synthesis procedures for systems containing plants subject to large parameter variations require that bounds (or boundaries) specifying the magnitude of these variations be produdec at each frequency of interest. This paper presents a direct method (the ‘ dominant chord ’ approach) of determining these (‘ strong ’) bounds, with little or no approximation, for a large class of plants. Additionally, it is shown that an extension of this method to produce ‘ weak ’ bounds can result in substantial reductions in loop gain requirements.