Comment: Compared to v2, we have in particular added an application (Section 4) and we now discuss the case of unbalanced panel data (Section 3.2)We consider fixed effects binary choice models with a fixed number of periods $T$ and regressors without a large support. If the time-varying unobserved terms are i.i.d. with known distribution $F$, \cite{chamberlain2010} shows that the common slope parameter is point identified if and only if $F$ is logistic. However, he only considers in his proof $T=2$. We show that the result does not generalize to $T\geq 3$: the common slope parameter can be identified when $F$ belongs to a family including the logit distribution. Identification is based on a conditional moment restriction. Under restrictions on the covariates, these moment conditions lead to point identification of relative effects. If $T=3$ and mild conditions hold, GMM estimators based on these conditional moment restrictions reach the semiparametric efficiency bound. Finally, we illustrate our method by revisiting Brender and Drazen (2008).