Why is it that children of immigrants often outdo their ethnic majority peers in educational aspirations yet struggle to keep pace with their achievements? This article advances the explanation that many immigrant communities, while positively selected on education, still have moderate absolute levels of schooling. Therefore, parents' education may imbue children with high expectations but not always the means to fulfill them. Swedish data on children of immigrants from over 100 countries of origin support this view: Net of parents' absolute years of schooling, a high rank in the sending country benefits children's aspirations, attitudes, and educational choices but not their test scores or school grades. The upshot is an ''aspiration squeeze'' where to emulate their parents' relative place in the education distribution, children are left struggling against the momentous tide of educational expansion.