Female choice for traits signaling male genetic quality is expected to erode heritable variation in fitness, undermining the benefits of choice. Known as the lek paradox, this contradiction has motivated extensive population genetic theory, yet remains unresolved. Recent modeling by Bonduriansky and Day concludes that costly female preference is best maintained when male condition is determined by environmentally induced factors transmitted across single generations. Here, we reformulate their model in explicitly epigenetic terms, and review evidence that environmentally induced paternal effects are mediated through epigenetic changes in sperm. Noncoding RNA expression, DNA methylation and histone modifications are highly sensitive to diet, stress, toxicants and stochastic events. Epigenetic variation renews each generation and cannot be exhausted by selection. By choosing well‐endowed males that produce gametes in epigenetically good states, females can increase their fitness directly through increased fertilization success or indirectly through epigenetic effects on the fitness of offspring and potentially subsequent generations.Also watch the video abstract.