The ability of prey to assess predation risk is fundamental to their success. It is routinely assumed predator cues do not vary in reliability across levels of predation risk. We propose that cues can differ in how precisely they indicate different levels of predation risk. What we call danger cues precisely indicate high risk levels, while safety cues precisely indicate low risk levels. Using optimality modeling, we find that prey fitness is increased when prey pay more attention to safety cues than danger cues. This fitness advantage is greatest when prey need to protect assets, predators are more dangerous, and predation risk increases at an accelerating rate with prey foraging efforts. Each of these conditions lead to prey foraging less when estimated predation risk is higher. Danger cues have less value than safety cues because they give precise information about risk when it is high, but prey behavior varies little when risk is high. Safety cues give precise information about levels of risk where prey behavior varies. These results highlight how our fascination with predators may have biased the way we study predator-prey interactions and focused too exclusively on cues that clearly indicate the presence of predator rather than cues that clearly indicate their absence.