A three-stage model isolates conditions under which an executive appointment to a collective choice body, such as a court or a regulatory agency, has an immediate bearing on policy. The model strikes a balance between previous formal models that predict either excessive gridlock or excessive policy responsiveness as a consequence of the politics of appointments. I test the model using approximately four decades of data on U.S. Supreme Court appointments. Two hypotheses summarize the unique predictions of the model and are strongly corroborated. A third, less distinctive hypothesis about strategic judicial retirements is weakly supported.