The procedure proposed by Buckley and James(1979)for estimating the regression coefficients in acensored data linear regression model has performed well in several studies and does not require distributional assumptions.Recently Hillis (1993) compares the finite sample properties of the methods proposed by Buckley and James(1979)Smith(1986)and Weissfeld and Schneider (1987) for estimatingthe covariance matrix of the Buckley James estimator and concludes that Smith's estimator is superior. However, Smith's method is defined only for the variance of the slope estimator in the simplelinear regression model. In this paper we consider a heuristic generalization of Smith's method tothe multiple linear regression model and compare the generalized Smith estimator with the Buckley James and WeissfeldSchneider estimators through simulations.The generalized version of Smith's method performs the best