Much work on optimal discrimination designs assumes that the models of interest are fullyspecified, apart from unknown parameters. Recent work allows errors in the models to be nonnormallydistributed but still requires the specification of the mean structures. Otsu (2008) proposedoptimal discriminating designs for semiparametric models by generalizing the Kullback–Leibleroptimality criterion proposed by López-Fidalgo et al. (2007). This paper develops a relativelysimple strategy for finding an optimal discrimination design.We also formulate equivalence theoremsto confirm optimality of a design and derive relations between optimal designs found herefor discriminating semiparametric models and those commonly used in optimal discriminationdesign problems.