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Multimodal communication has received increasing attention in recent years. While much is understood about how intended receivers (such as potential mates) respond to multimodal displays, less is known about how eavesdropping predators perceive and interpret these cues. The male túngara frog, Physalaemus pustulosus, is a neotropical anuran that attracts females with an acoustic call and a dynamically inflating/deflating vocal sac. However, the túngara frog's multimodal courtship display also attracts eavesdropping predators, such as fringe-lipped bats, Trachops cirrhosus. We utilized robotic frog models to expose fringe-lipped bats to multimodal túngara frog courtship displays. The models varied in call amplitude and/or the presence of vocal sac cues. In a two-choice test, we show that fringe-lipped bats more often attack higher-amplitude calls. Additionally, coupling the inflating vocal sac cues to the lower-amplitude frog call increased the probability that a bat would attack this less attractive call. Previous studies have demonstrated that vocal sac cues do not increase the attractiveness of low-amplitude calls to female P. pustulosus. Thus, although natural selection, through the bats, and sexual selection, through the female frogs, exert counter-selection forces on the male's sexual display, the strength of these forces are not symmetrical. We discuss possible explanations for why this might be the case. This study underlines the importance of understanding the contribution of both intended and unintended receivers on signal evolution, and it helps explain how selection pressures might vary across sensory modalities.