In the Vietnam and Iraq conflicts, British Prime Ministers were asked to contribute forces to an American-led war that was deeply unpopular in the United Kingdom. This presented Harold Wilson and Tony Blair with conflicting incentives and constraints: to support their senior ally or to make policy based upon domestic considerations. Why did Harold Wilson decline to commit British forces while Tony Blair agreed to do so? With situational factors generating conflicting predictions, I argue that investigation of individual-level variables is necessary. In particular, I suggest that leaders vary systematically in their willingness to subordinate the concerns of constituents to strategic imperatives, and that introducing the leadership style categories of “constraint challenger” and “constraint respecter” can make more determinate the linkage between domestic politics and strategic concerns.