The sonar systems of bats and dolphins are in many ways superior to man-made sonar and radar systems, and considerable effort has been devoted to understanding the signal-processing strategies underlying these capabilities. A major feature determining the efficiency of sonar systems is the sensitivity to noise and jamming signals. Previous studies indicated that echolocating bats may adjust their signal structure to avoid jamming (‘jamming avoidance response’; JAR). However, these studies relied on behavioural correlations and not controlled experiments. Here, we provide the first experimental evidence for JAR in bats. We presented bats (Tadarida brasiliensis) with ‘playback stimuli’ consisting of recorded echolocation calls at one of six frequencies. The bats exhibited a JAR by shifting their call frequency away from the presented playback frequency. When the approaching bats were challenged by an abrupt change in the playback stimulus, they responded by shifting their call frequencies upwards, away from the playback. Interestingly, even bats initially calling below the playback's frequency shifted their frequencies upwards, ‘jumping’ over the playback frequency. These spectral shifts in the bats' calls occurred often within less than 200 ms, in the first echolocation call emitted after the stimulus switch—suggesting that rapid jamming avoidance is important for the bat.