Scholars of public opinion on military intervention agree that survey respondents make judgments from limited information. Yet researchers still question whether ordinary Americans reflect elite attitudes or instead reach their own “pretty prudent” conclusions from the stated principal policy objective (PPO). This article adjudicates the debate while incorporating lessons from the study of bounded rationality. Evidence comes from an original data set of aggregate US public opinion, covering 1,080 nationally representative survey items about launching operations, across thirty-five countries, during 1981 to 2016. Tests show that PPO matters: pursuing “internal policy change” is less popular than restraining international aggression. However, language reflecting White House cues and one prominent cognitive shortcut (the “availability heuristic”) statistically and substantively outperforms PPO at predicting intervention support. The results indicate that when ordinary Americans are polled about using force against salient foes (Saddam Hussein, al-Qaeda, Islamic State in Iraq and Syria), elements of bounded rationality can overtake the prudence expressed toward less vivid problems.