'Sophisticated voting' has a solid theoretical foundation, but scholars have raised serious questions about its empirical importance in real-world institutions. The U.S. Supreme Court is one institution where sophisticated voting should be common, but, paradoxically, where scholarly consensus about its existence has yet to emerge. We develop and test a formal model of sophisticated voting on agenda setting in the Supreme Court. Using data on petitions for certiorari decided in October term 1982, we show that, above and beyond the usual forces in case selection, justices engage in sophisticated voting, defined as looking forward to the decision on the merits and acting with that potential outcome in mind, and do so in a wide range of circumstances. In particular, we present strong evidence for sophisticated behavior, ranging from votes to deny a case one prefers to reverse to votes to grant cases one prefers to affirm. More importantly, sophisticated voting makes a substantial difference in the size and content of the Court's plenary agenda.