When zero mean measurement error is added to the dependent variable for the nonlimit observations of the censored normal regression model, the conventional maximum likelihood estimator (Tobit) is inconsistent. "Correct" maximum likelihood estimation appears to be computationally difficult under various specifications for the distribution of the measurement error. Estimators based on either the expectation function or the conditional expectation function for uncensored observations remain consistent in the presence of measurement error. Eight such estimators are examined. The results of a numerical experiment suggest that several of these estimators are substantially more efficient than the conventional maximum likelihood estimator when measurement error exists and that they also will do reasonably well when it does not.