The ability to veto legislation is the most important formal power of the presidency in the legislative process, and presidents’ veto behavior has thus attracted a great deal of theoretical interest. Game-theoretic models of congressional—presidential interactions explain vetoes by incorporating incomplete information over the distribution of presidential or congressional types. In this article, I examine two prominent such theories, as well as a simple “noisy” extension of a complete information theory. I show that each makes strong predictions not only about vetoes themselves but also about the resulting override votes; given that overrides are so closely connected with vetoes, any valid theory of the latter must be able to successfully explain the former. I test these predictions empirically and show that support for each of these theories in presidential veto and override data from 1973 to 2008 is quite weak. This negative result suggests that current models of the veto are incomplete; I sketch some possibilities for extension in the conclusion.