1) The integration of immigrants should be measured by both disadvantage (differences in outcomes between immigrants and natives) and penalty (differences that remain after controlling for personal characteristics). 2) Longitudinal data is needed to properly evaluate integration over time, but such data is lacking in Italy. Cross-sectional data using "years since migration" as a proxy is flawed. 3) Differences in living conditions between families with all immigrants and mixed families were surprisingly small, raising questions about composition effects.