We studied a brood parasite-host system (the cuckoo finch Anomalospiza imberbis and its host, the tawny-flanked prinia Prinia subflava) to test (1) the fundamental hypothesis that deceptive mimics evolve to resemble models, selecting in turn for models to evolve away from mimics ('chase-away evolution') and (2) whether such reciprocal evolution maintains imperfect mimicry over time. Over only 50 years, parasites evolved towards hosts and hosts evolved away from parasites, resulting in no detectible increase in mimetic fidelity. Our results reflect rapid adaptive evolution in wild populations of models and mimics and show that chase-away evolution in models can counteract even rapid evolution of mimics, resulting in the persistence of imperfect mimicry.