Quasispecies theory is a case of mutation-selection balance for evolution at high mutation rates, such as those observed in RNA viruses. One of the main predictions of this model is the selection for robustness, defined as the ability of an organism to remain phenotypically unchanged in the face of mutation. We have used a collection of vesicular stomatitis virus strains that had been evolving either under positive selection or under random drift. We had previously shown that the former increase in fitness while the latter have overall fitness decreases (I. S. Novella, J. B. Presloid, T. Zhou, S. D. Smith-Tsurkan, B. E. Ebendick-Corpus, R. N. Dutta, K. L. Lust, and C. O. Wilke, J. Virol. 84:4960-4968, 2010). Here, we determined the robustness of these strains and demonstrated that strains under positive selection not only increase in fitness but also increase in robustness. In contrast, strains under drift not only decreased in fitness but also decreased in robustness. There was a good overall correlation between fitness and robustness. We also tested whether there was a correlation between fitness and thermostability, and we observed that the correlation was imperfect, indicating that the fitness effects of mutations are exerted in part at a level other than changing the resistance of the protein to temperature.