Lekking males are thought to face strong directional selection on secondary sexual traits. How variation in male traits can persist under these conditions remains problematic (the lek paradox). Here, we present several game-theoretic models that show that avoidance of costly and mobile predators, sneakers, or brood parasites (enemies) leads to variation in female choice. This can result in maintenance of variation in male quality. "Enemies" will congregate around higher quality males. Females must then trade-off the benefits of mating with high-quality males against the increased risk of enemies. At equilibrium, the models predict a positive correlation between the quality of a male and the proportions of both enemies and females visiting him. In the first model, we use this framework to predict the lowest quality male on the lek that will receive any matings. In the second model, we examine the influence of this female-enemy game on the maintenance of variation in male quality. Low-quality males are likely to persist when enemies are costly to females or occur at high density, and when there is some spatial structure on the lek, so that neighboring males are typically of similar quality. If enemies are more costly to males than to females, high-quality males may benefit from receiving fewer female visits. In the third model, we consider the special case when enemies are male reproductive parasites. These models illustrate the importance of considering the simultaneous decisions of multiple players in mate choice games.