Choice-based samples oversample infrequently chosen alternatives to obtain an effective representation of the behavior of people who select these alternatives. However, the use of choice-based samples requires recognition of the sampling process in formulating the estimation procedure. In general, this procedure can be accomplished by applying weights to the observed choices in the estimation process. Unfortunately, the use of such weighted estimation procedures for choice models does not yield efficient estimators. However, for the special case of the multinomial logit model with a full set of alternative-specific constants, the standard maximum likelihood estimator - which is efficient - can be used with adjustment of the alternative-specific constants. The same maximum likelihood estimator can also be used with adjustment to estimate nested logit models with choice-based samples. The proof of this property is qualitatively described, and examples demonstrate how to apply the adjustment procedure.