Suicide attacks have raised the stakes for officers deciding whether or not to shoot a suspect (‘Police Officer's Terrorist Dilemma’). Despite high-profile errors we know little about how trust in the police is affected by their response to the terrorist threat. Building on a conceptualisation of lay observers as intuitive signal detection theorists, a general population sample (N = 1153) were presented with scenarios manipulated in terms of suspect status (Armed/Unarmed), officer decision (Shoot/Not Shoot) and outcome severity (e.g. suspect armed with Bomb/Knife; police shoot suspect/suspect plus child bystander). Supporting predictions, people showed higher trust in officers who made correct decisions, reflecting good discrimination ability and who decided to shoot, reflecting an ‘appropriate’ response bias given the relative costs and benefits. This latter effect was moderated by (a) outcome severity, suggesting it did not simply reflect a preference for a particular type of action, and (b) preferences for a tough stance towards terrorism indexed by Right-Wing Authoritarianism (RWA). Despite loss of civilian life, failure to prevent minor terror attacks resulted in no loss of trust amongst people low in RWA, whereas among people high in RWA trust was positive when police erroneously shot an unarmed suspect. Relations to alternative definitions of trust and procedural justice research are discussed. Copyright © 2007 John Wiley & Sons, Ltd.