Deception is common in nature, but victims of deception discriminate against and ultimately ignore deceptive signals when they are produced too frequently. Flexible variation of signals could allow evasion of such constraints. Fork-tailed drongos (Dicrurus adsimilis) use false alarm calls to scare other species away from food that they then steal. We show that drongos mimic the alarms of targeted species. Further, target species reduce their response to false alarm calls when they are repeated. However, the fear response is maintained when the call is varied. Drongos exploit this propensity by changing their alarm-call type when making repeated theft attempts on a particular species. Our results show that drongos can evade the frequency-dependent constraints that typically limit deception payoffs through flexible variation of their alarm calls.