In this paper several alternative robust reqression techniques are compared for estimating parameters of a Weibull distribution . In addition to the usual least squares (L2) and least absolute deviation (L1) methods, a number of one-step reweighting schemes based on the L1residuals are considered. The results of an extensive series of Monte Carlo simulation experiments demonstrate that the Anscmbe reweighting scheme generally produces the best Weibull estimates over the range of sample sizes and parameter values studied.