Eavesdropping predators sometimes show preferences for certain prey signal variants, yet the ultimate and proximate reasons for such preferences are often unclear. The fringe-lipped bat, Trachops cirrhosus, eavesdrops on the advertisement calls of male túngara frogs, Physalaemus pustulosus, and shows a marked preference for complex (adorned) calls over simple (non-adorned) calls. We hypothesized that this preference stems from perceptual biases in the sensory and/or cognitive systems of T. cirrhosus. To test this hypothesis, we conducted a series of preference experiments in which we presented bats with various modified simple calls, each altered to possess one of the acoustic properties that distinguish complex calls from simple calls. We reasoned that if perceptual bias accounts for the bat's preference for complex calls, then a novel stimulus with similar acoustic properties to the complex call should be attractive as well (i.e., the preference should be permissive). Except for weak evidence suggesting that the longer duration of complex calls could contribute to their greater attractiveness to T. cirrhosus, we did not find any indication that perceptual biases account for this eavesdropper preference. Instead, we suggest that T. cirrhosus developed their preference for call complexity because eavesdropping on complex calls provides greater fitness benefits than eavesdropping on simple calls, for example, because eavesdropping on complex calls may increase probability of prey capture and/or lead to more profitable food patches.