Imperfect synchrony between male calls occurs widely in acoustically courting crickets and bushcrickets. Males which are able to establish the temporal leadership usually attract more females in choice experiments but the proximate mechanism for this precedence effect is unknown. Here we show that contralateral inhibition, the neural basis for lateral contrast enhancement in the auditory pathways of insects and vertebrates, is also the probable proximate neural mechanism for this female preference. We recorded simultaneously from a pair of identified auditory interneurons in the synchronizing bushcricket Mecopoda elongata. When two identical acoustic stimuli are presented from opposite directions, one preceding the other by 120 ms, the neural representation within the receiver is far stronger for the leader signal. This results from a suppression of the neural response to the follower chirp by reciprocal contralateral inhibition. The advantage of the representation of the leader is 2–3-fold with time delays between 70 and 130 ms; the most clear-cut female preferences have also been found with such delays in previous behavioural experiments. In time–intensity trading experiments, a lead by 120 ms could only be compensated for by increasing the amplitude of the follower signal by 7–11 dB. We discuss contralateral inhibition in auditory systems as a sensory bias that results in female preference for leading signals, with important evolutionary consequences for male calling strategies.