A standard assumption in the literature on judicial behavior holds that decisions of multimember courts conform to the preferences of the median judge. Judges and scholars have suggested, however, that contrary to the predictions of the median voter theorem, the judge with the power to assign the panel opinion wields disproportionate influence over case outcomes. In this article, we investigate whether the “assignment power” systematically affects outcomes on three-judge panels in the 13 federal circuits. We identify which judge presides over the panel in more than 126,000 cases across all circuits between 1993 and 2007. We exploit cross-circuit variation in the allocation of the assignment power to disentangle the effect of assignment from other attributes of presiding judges. We find that the judge who wields the assignment power is significantly less likely than other judges to dissent—an indication that assigning judges are more likely to be satisfied with the case outcome. We find evidence that assigning judges influence case outcomes through strategic assignment of opinions to other panel members, but no evidence that assigning judges influence case outcomes through strategic self-assignment of majority opinions. Our results suggest that decisionmaking on multimember courts is shaped not only by the composition of panels but also by the allocation of the assignment power among panel members.