An increasingly common practice across the world is to introduce private alternatives into publically funded education systems. Economists have found that following from this practice, private schools often engage in what is called “cream skimming”, where they attract solely the most highly able students and thereby worsen the socio-economic stratification of the education system. In this paper, we argue that under conditions where for-profit schools are allowed, but they only receive a flat voucher per student, the phenomenon of “reverse cream skimming” where private schools selectively target the least motivated students is a likely outcome. We show this to be the case in a quantitative analysis of admissions to the secondary schools in a Swedish municipality from 1999 to 2017. Implications for theories of how schools compete, public education policy, and for institutional theory are discussed.