Abstract Animals often use assessment signals to communicate information about their quality to a variety of receivers, including potential mates, competitors, and predators. But what maintains reliable signaling and prevents signalers from signaling a better quality than they actually have? Previous work has shown that reliable signaling can be maintained if signalers pay fitness costs for signaling at different intensities and these costs are greater for lower quality individuals than higher quality ones. Models supporting this idea typically assume that continuous variation in signal intensity is perceived as such by receivers. In many organisms, however, receivers have threshold responses to signals, in which they respond to a signal if it is above a threshold value and do not respond if the signal is below the threshold value. Here, we use both analytical and individual-based models to investigate how such threshold responses affect the reliability of assessment signals. We show that reliable signaling systems can break down when receivers have an invariant threshold response, but reliable signaling can be rescued if there is variation among receivers in the location of their threshold boundary. Our models provide an important step towards understanding signal evolution when receivers have threshold responses to continuous signal variation.