This paper integrates the literatures on judicial compliance, panel decision making and case selection in the federal judiciary hierarchy. Many studies have speculated that ``panel effects" -- the phenomena under which an individual judge's vote may depend on her colleagues on a three-judge panel -- can be tied to a ``whistleblower effect," through which a lower court judge can constrain a panel majority from disobeying with Supreme Court precedent by threatening to dissent. However, no study has systematically found such a relationship. I present a game-theoretic model of circuit court-Supreme Court interaction that demonstrates how panel composition might affect the likelihood of lower court compliance to Supreme Court doctrine. The model illustrates how three-judge panels, while not inducing perfect doctrinal control of lower courts by the Supreme Court, significantly increases the latter's ability to see its preferred doctrine carried out by its subordinates in the judicial hierarchy.