Target prevalence powerfully influences visual search behavior. In most visual search experiments, targets appear on at least 50% of trials [1-3]. However, when targets are rare (as in medical or airport screening), observers shift response criteria, leading to elevated miss error rates [4, 5]. Observers also speed target-absent responses and may make more motor errors [6]. This could be a speed/accuracy tradeoff with fast, frequent absent responses producing more miss errors. Disproving this hypothesis, our experiment one shows that very high target prevalence (98%) shifts response criteria in the opposite direction, leading to elevated false alarms in a simulated baggage search. However, the very frequent target-present responses are not speeded. Rather, rare target-absent responses are greatly slowed. In experiment two, prevalence was varied sinusoidally over 1000 trials as observers' accuracy and reaction times (RTs) were measured. Observers' criterion and target-absent RTs tracked prevalence. Sensitivity (d') and target-present RTs did not vary with prevalence [7-9]. These results support a model in which prevalence influences two parameters: a decision criterion governing the series of perceptual decisions about each attended item, and a quitting threshold that governs the timing of target-absent responses. Models in which target prevalence only influences an overall decision criterion are not supported.