The finite sample properties of an asymptotically efficient technique (JASA, June, 1962) for estimating coefficients in certain generally encountered sets of regression equations are studied in this paper. In particular, exact first and second moments of the asymptotically efficient coefficient estimator are derived and compared with those of the usual least squares estimator. Further, the exact probability density function of the new estimator is derived and studied as a function of sample size. It is found that the approach to asymptotic normality is fairly rapid and that for a wide range of conditions an appreciable part of the asymptotic gain in efficiency is realized in samples of finite size.