This study addressed 2 issues of using loglinear models for smoothing univariate test score distributions and for enhancing the stability of equipercentile equating functions. One issue was a comparative assessment of several statistical strategies that have been proposed for selecting 1 from several competing model parameterizations. Another issue was an evaluation of the influence of the selection strategies on equating function accuracy. These issues were considered in a simulation study, where the accuracies of 17 selection strategies for loglinear models and their effects on equating function accuracies were assessed across a range of sample sizes, test score distributions, and population equating functions. The results differentiate the selection strategies in terms of their accuracies in selecting correct model parameterizations and define the situations where their use has the most important implications for equating function accuracy.