Buckley and James's (1979)) procedure has been shown to be an effective method for estimating the regression coefficients in a censored data linear regression model without requiring distributional assumptions. However, relatively little attention has been given to studying the finite sample properties of proposed methods for estimating the covariance matrix of the Buckley-James estimator. The purpose of this paper is to compare the finite sample properties of the variance estimation methods proposed by Buckley and James (1979), Smith (1986), and Weissfeld and Schneider (1987) for a broad range of error and censoring distributions. We conclude that for moderate sample sizes Smith's estimator performs the best; primarily because of its instability, we rate the Buckley-James variance estimator as the least desirable of the three methods.