Sperm morphology varies enormously across the animal kingdom. Whilst knowledge of the factors that drive the evolution of interspecific variation in sperm morphology is accumulating, we currently have little understanding of factors that may constrain evolutionary change in sperm traits. We investigated whether susceptibility to sperm abnormalities could represent such a constraint in songbirds, a group characterized by a distinctive helical sperm head shape. Specifically, using 36 songbird species and data from light and scanning electron microscopy, we examined among‐species correlations between the occurrence of sperm head abnormalities and sperm morphology, as well as the correlation between sperm head abnormalities and two indicators of sperm competition. We found that species with more helically shaped sperm heads (i.e., a wider helical membrane and more pronounced cell waveform) had a higher percentage of abnormal sperm heads than species with less helical sperm (i.e., relatively straight sperm) and that sperm head traits were better predictors of head abnormalities than total sperm length. In contrast, there was no correlation between sperm abnormalities and the level of sperm competition. Given that songbird species with more pronounced helical sperm have higher average sperm swimming speed, our results suggest an evolutionary trade‐off between sperm performance and the structural integrity of the sperm head. As such, susceptibility to morphological abnormalities may constrain the evolution of helical sperm morphology in songbirds.