Migration is a complex trait although little is known about genetic correlations between traits involved in such migration syndromes. To assess the migratory responses to climate change, we need information on genetic constraints on evolutionary potential of arrival dates in migratory birds. Using two long-term data sets on barn swallows Hirundo rustica (from Spain and Denmark), we show for the first time in wild populations that spring arrival dates are phenotypically and genetically correlated with morphological and life history traits. In the Danish population, length of outermost tail feathers and wing length were negatively genetically correlated with arrival date. In the Spanish population, we found a negative genetic correlation between arrival date and time elapsed between arrival date and laying date, constraining response to selection that favours both early arrival and shorter delays. This results in a decreased rate of adaptation, not because of constraints on arrival date, but constraints on delay before breeding, that is, a trait that can be equally important in the context of climate change.