We employ a combination of school fixed effects and IV estimation to estimate the effect of class size on student performance in 18 countries. Using the random part of the class-size variation between two adjacent grades within individual schools allows us to identify causal class-size effects. Conventional estimates of class-size effects are shown to be severely biased in most school systems by within- and between-school sorting of students. Differences in our estimates across countries suggest that it is misleading to generalize results from one school system to others. While we find sizable beneficial effects of smaller classes in Greece and Iceland, the possibility of even small effects is rejected in Japan and Singapore. In 11 countries, we rule out large class-size effects. The existence of class-size effects, and the lack thereof, in different school systems appears to be related to the relative quality of the teaching force.