Recently Dunne (2010) and Dronkers, van der Velden & Dunne (2011) introduced a three-level model: countries, schools, and students. They showed that school characteristics like socioeconomic composition and ethnic diversity have substantial effects on achievement levels and also affect the relation between parental background and achievement. Moreover, these school characteristics seem to mediate some of the effects of educational system characteristics found earlier (see Figure 1). However their results contradict very much the consensus about the effects of educational systems on outcomes and inequality, which are exclusively based on a two-level model: countries and students. The most important authors are Hanushek and Wößmann (2006), Schütz, Ursprung and Wößmann (2008), Wößmann, Lüdemann, Schütz and West (2009) and Hanushek and Wößmann (2012). Esser (forth coming) discussed rightfully extensively the possible explanations of the different outcomes of the Hanushek & Wössmann approach and the Dronkers, van der Velden & Dunne puzzle.