We estimate the effect of class size on student performance in 11 countries, combining school fixed effects and instrumental variables to identify random class-size variation between two adjacent grades within individual schools. Conventional estimates of class-size effects are shown to be severely biased by the non-random placement of students between and within schools. While we find sizable beneficial effects of smaller classes in Greece and Iceland, we reject the possibility of even small effects in four countries and of large beneficial effects in an additional four countries. Noteworthy class-size effects are observed only in countries with relatively low teacher salaries.