One complication in studying the Supreme Court and the judicial hierarchy is that the Court's docket is now nearly completely discretionary. Although the Justices’ strategies in picking cases affect the observations we make and the inferences we draw, this is rarely taken into account in studies of judicial politics. In this article, we study how case selection can affect our inferences within judicial politics, including those about decision making in the Supreme Court itself (such as whether law constrains the Justices) and throughout the judicial hierarchy (such as whether lower courts comply with Supreme Court doctrine). We use simulation analysis to show that the inferential problems raised by the Court's case selection range from moderate to severe. At stake are substantive conclusions within some of the most important and controversial debates in judicial politics.