This paper compares various methods of smoothed equipercentile equating and linear equating in the random groups equating design. Three presmoothing methods (based on the beta binomial model, four-parameter beta binomial model and a log-linear model) are compared to postsmoothing using cubic splines, linear equating and unsmoothed equipercentile equating. Performance of these methods is evaluated by specifying several pairs of population distributions and estimating the equating error by Monte Carlo methods. The results indicate that both presmoothing and postsmoothing methods can improve estimation of the equipercentile equating function and that presmoothing and postsmoothing methods provide comparable levels of performance in terms of equating error. (Contains 13 references, 7 tables, and 15 figures.) (Author)