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Background Certainty of paternity is considered an important factor in the evolution of paternal care. Several meta-analyses across birds support this idea, particularly for species with altricial young. However, the role of certainty of paternity in the evolution and maintenance of exclusive paternal care in the black coucal (Centropus grillii), which is the only known altricial bird species with male-only care, is not well understood. Here we investigated whether the differences in levels of paternal care in the black coucal and its sympatric congener, the bi-parental white-browed coucal (Centropus superciliosus), are shaped by extra-pair paternity. Results We found that male black coucals experienced a substantially higher loss of paternity than white-browed coucals. Further, unlike any previously reported bird species, extra-pair offspring in black coucals represented mainly the last hatchlings of the broods, and these last hatchlings were more likely to disappear during partial-brood loss. Conclusion The results suggest that exclusive paternal care in black coucals is not maintained by male certainty of parentage, and extra-pair fertilizations are unlikely to be a female strategy for seeking ‘good genes’. Extra-pair paternity in black coucals may reflect the inability of males to guard and copulate with the female after the onset of incubation, and a female strategy to demonstrate her commitment to other males of her social group. Electronic supplementary material The online version of this article (10.1186/s12862-018-1225-y) contains supplementary material, which is available to authorized users.