Qualitative and multimethod scholars face a wide and often confusing array of alternatives for case selection using the results of a prior regression analysis. Methodologists have recommended alternatives including selection of typical cases, deviant cases, extreme cases on the independent variable, extreme cases on the dependent variable, influential cases, most similar cases, most different cases, pathway cases, and randomly sampled cases, among others. Yet this literature leaves it substantially unclear which of these approaches is best for any particular goal. Via statistical modeling and simulation, I argue that the rarely considered approach of selecting cases with extreme values on the main independent variable, as well as the more commonly discussed deviant case design, are the best alternatives for a broad range of discovery-related goals. By contrast, the widely discussed and advocated typical case, extreme-on-Y, and most similar cases approaches to case selection are much less valuable than scholars in the qualitative and multimethods research traditions have recognized to date.