This article describes a Monte Carlo study of 2 methods for treating incomplete non-normal data. Skewed, kurtotic data sets conforming to a single structured model, but varying in sample size, percentage of data missing, and missing-data mechanism, were produced. An asymptotically distribution-free available-case (ADFAC) method and structured-model expectation-maximization (EM) with non-normality corrections were applied to these data sets, and the 2 methods were then compared in terms of bias in parameter estimates, bias in standard-error estimates, efficiency of parameter estimates, and model chi-squares. The results favored the non-normality corrected EM over the ADFAC method in almost all respects, the only important exception involving bias in standard-error estimates with large samples.