We exploit rules of class formation to identify the causal effect of increasing the number of immigrants in a classroom on natives test scores, keeping class size constant (Pure Composition Effect). We explain why this is a relevant policy parameter although it has been neglected so far. We show that the PCE is sizeable and negative at age 7 (-1.6% for language and math) and does not vanish when children grow up to age 10. Conventional estimates are instead smaller because they are confounded by endogenous class size adjustments implemented by principals when confronted with immigrant and native inflows.