Evolutionary lag and resistance to puncture-ejection are two hypotheses explaining why hosts long exposed to brood parasitism by molothrine cowbirds accept their eggs. The former hypothesis assumes no physical constraints while the latter requires them. We show (1) that most acceptors of Brown-headed Cowbird eggs have small bills, (2) that the single species known to puncture cowbird eggs for ejection also has a small bill, and (3) that all grasp ejectors of Brown-headed Cowbird eggs have large bills. We propose that most acceptors cannot remove cowbird eggs by grasp ejection because their bills are too small. Small hosts probably cannot puncture cowbird eggs for ejection because their unusually thick shells make the costs of puncturing them higher than the benefits of ejection. This hypothesis is capable of explaining the success of cowbirds with scores of host species in the puzzling absence of egg mimicry.