The effectiveness of 19 methods of smoothing was investigated as those methods apply to the equipercentile method of test equating. Seven methods involved smoothing the score distribution before the tests were equated (presmoothing). Seven involved smoothing the resultant points after the equating (postsmoothing). Five methods involved combining presmoothers and postsmoothers. The results of smoothing were evaluated by comparing smoothed and unsmoothed equatings with large sample equating or other criterion equatings. The data that were used include the results of test simulations and results of administrations of military selection tests. Measure of average absolute deviation, average signed deviation, and root mean square deviation were calculated. Jackknifing was also used to estimate standard errors of equatings. The nonlinear presmoothers were less effective than a presmoother based on negative hypergeometric distribution. Among the postsmoothers, the most promising was a technique using cubic smoothing splines. Combining presmoothers and postsmoothers was not notably more effective than either smoother alone. It is suggested that the family of smoothing functions based on the negative hypergeometric be more fully investigated. (Author)