For a gleaning bat hunting prey from the ground, rustling sounds generated by prey movements are essential to invoke a hunting behaviour. The detection of prey-generated rustling sounds may depend heavily on the time structure of the prey-generated and the masking sounds due to their spectral similarity. Here, we systematically investigate the effect of the temporal structure on psychophysical rustling-sound detection in the gleaning bat, Megaderma lyra. A recorded rustling sound serves as the signal; the maskers are either Gaussian noise or broadband noise with various degrees of envelope fluctuations. Exploratory experiments indicate that the selective manipulation of the temporal structure of the rustling sound does not influence its detection in a Gaussian-noise masker. The results of the main experiment show, however, that the temporal structure of the masker has a strong and systematic effect on rustling-sound detection: When the width of irregularly spaced gaps in the masker exceeded about 0.3 ms, rustling-sound detection improved monotonically with increasing gap duration. Computer simulations of this experiment reveal that a combined detection strategy of spectral and temporal analysis underlies rustling-sound detection with fluctuating masking sounds.