Consonance sets are obtained by inverting inequalities for goodness-of-fit statistics which are considered as functions of the parameters of a model distribution. In this paper we present some evidence to indicate that the use of the Kolmogorov-Smimov statistic assures reasonable results for location and scale parameters. Specifically, the consonance sets obtained are convex and finite. The development also provides a method for set construction. An example shows that the discrete X2statistic does not in general yield convex sets.