A rich data set gives a unique opportunity to study heterogeneity in intergenerational mobility. Here, we explore whether the intergenerational association in education and income is the same for children with different results in a cognitive ability test (the Swedish Military Enlistment test). Despite an endogenous test score, the argument is that this is the policy relevant case to analyze, i.e. whether children of a certain cognitive ability level are influences by their parents' socioeconomic status and not whether they are influenced by some random parent. The intergenerational associations vary a great deal with the results in the cognitive ability test. The intergenerational association is highest for the middle ability groups and lower for both the higher ability and (particularly) the lower ability groups. The overall conclusion is that adding the cognitive ability dimension to studies of intergenerational mobility contributes new and important insights. For example, since the average child (cognitively speaking) seems to be most receptive to parental influence, intergenerational mobility is primarily increased by targeting the average child.