We estimate intergenerational income mobility in the US and Sweden, using a new nonparametric approach. The approach addresses several empirical issues raised in the literature and applies when other estimators are infeasible. We argue that previous estimates of income mobility conceal the heterogeneous nature of the transmission mechanism by keeping mobility constant across families. The striking differences we find between mobility patterns across family backgrounds, captured by father's education, lead us to question the conventional result that intergenerational transmission of earnings is weaker in Sweden than in the United States, for important parts of the population.