There is a large literature on how leaders and their advisors can best make difficult decisions, generally seen as ones informationally or technically complex, or requiring value tradeoffs. Much of this literature centers on the dangers of “groupthink,” where a group rushes to judgment too quickly, without hearing dissent and consideration of alternatives. The remedy is seen as “vigilant decision-making,” where the leader encourages wide consideration of alternatives and is open to dissenting viewpoints. We senior executives in the U.S. federal government, asking questions about how they made their most difficult decisions. We were initially focused on whether they employed a vigilant approach or not. However, we found that most executives identified their most difficult decision as one that was not complex, but rather required courage: the hard thing was not deciding what the right thing to do was, but to do it. We also found that they made decisions requiring courage in ways very different from those recommended by the vigilant decision-making paradigm. We thus develop a contingency model of effective executive decision-making that requires leaders to be “ambidextrous” and use different techniques to make complex deci sions and ones requiring courage.