Because of its less restrictive assumptions, the equi-percentile method of equating is theoretically preferable to the mean-and-sigma method; unfortunately it involves more sampling error. The Cureton-Tukey procedure for reducing this sampling error by mathematically "smoothing" the samples before equating by the equi-percentile method is described, and empirically evaluated. Although the Cureton-tukey procedure seems promising, none of the differences among the three methods being compared -- the mean-and-sigma method, the equi-percentile method, and the Cureton-Tukey method -- reach statistical significance. It is therefore impossible to draw any definitive conclusions from the limited data employed in this study.