Much work on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters. Recent work allows errors in the models to be nonnormally distributed but still requires the specification of the mean structures.Otsu (2008) proposed optimal discriminating designs for semiparametric models by generalizing the Kullback-Leibler optimality criterion proposed byLópez-Fidalgo et al. (2007). This paper develops a relatively simple strategy for finding an optimal discrimination design. We also formulate equivalence theorems to confirm optimality of a design and derive relations between optimal designs found here for discriminating semiparametric models and those commonly used in optimal discrimination design problems.