The paper looks at how segregation mechanisms in the primary school system can aggravate social inequality. School segregation (teaching students with different social background in different schools or different classrooms) can emerge in many ways. It can be initiated by local authorities, but laissez-faire or universal voucher system is also likely to lead to segregation if parents are free to choose schools and schools are free to choose students. There are documented cases of segregation in the first way in Hungary, but the second way is even more important, as the Hungarian primary school system is close to a universal voucher model. Based on economic theory and international evidence, the paper argues that in a segregated environment, children from disadvantaged families are bound to receive education of a lower quality than they would in a more integrated environment. Besides peer effects, lower-quality teaching in classrooms with more disadvantaged students is a necessary consequence if teachers are not compensated for the extra work - as they are not in Hungary. Hungarian data are scarce, but the available evidence suggests that primary schools have become more unequal since 1989, which has led to more unequal student outcomes. Correlation of family background and student outcomes is extremely strong in Hungary, by international comparison. Unequal primary schooling is probably an important factor in creating that correlation. Hungarian primary schools therefore play a significant role in increasing inherited inequality, which is clearly detrimental for efficiency and moral reasons.