We investigate the effect of changing the population size of one predator species on the fitness of another predator when both share a common prey species. The prey is assumed to have different anti-predator behaviors for each predator. Anti-predator behavior can result in one or both predators having positive effects on the fitness of the other. Positive short-term effects (on a behavioral time scale) can be produced by three mechanisms: (1) A behavior that defends against one predator may make the prey more vulnerable to the other; (2) Increased defensive behavior against one predator may increase the cost of defense against the other, resulting in a reduction in the latter defense; (3) If the prey constantly employs some anti-predator behavior, an increase in one behavior can only come at the expense of a reduction in another. The long-term effect of one predator on another is more likely to be negative than is the short-term effect, due to reduction in prey density. However, a strongly positive short-term effect and a prey population that is weakly affected by predator density, can produce a positive long-term effect. Even when both short- and long-term interactions between predators are competitive, the prey's behavior often reduces the ratio of inter- to intra-specific competition between the two predators, promoting their coexistence.