If the disturbances of a linear regression model are skewed and/or thick-tailed, a maximum likelihood estimator is efficient relative to the customary Ordinary Least Squares (OLS) estimator. In this paper, we specify a highly flexible Generalized Tukey Lambda (GTL) distribution to model skewed and thick-tailed disturbances. The GTL-regression estimator is consistent and asymptotically normal. We demonstrate the potential gains of the GTL estimator over the OLS estimator in a Monte Carlo study and in five applications that are typical of applied economics research problems: log-wage equations, hedonic housing price equations, an analysis of speeding tickets, the issue of trade creation and trade diversion that result from preferential trade agreements, and the familiar CAPM model in financial economics.