Least squares estimators for the threshold, scale, and shape parameters of the Weibull distribution are developed. Results of simulation studies that were conducted to compare the performances of least squares estimates with the moments, maximum likelihood, modified moments, and modified maximum likelihood estimates of Cohen and Whitten (1982) are presented. This study will show that least squares estimates are comparable with, or better than, other alternative ways of making estimates. Since least squares estimates are always applicable, their use for samples of small to moderate size is recommended.