Parallel analysis (PA) is a useful empirical tool for assessing the number of factors in exploratory factor analysis. On conceptual and empirical grounds, we argue for a revision to PA that makes it more consistent with hypothesis testing. Using Monte Carlo methods, we evaluated the relative accuracy of the revised PA (R-PA) and traditional PA (T-PA) methods for factor analysis of tetrachoric correlations between items with binary responses. We manipulated five data generation factors: number of observations, type of factor model, factor loadings, correlation between factors, and distribution of thresholds. The R-PA method tended to be more accurate than T-PA, although not uniformly across conditions. R-PA tended to perform better relative to T-PA if the underlying model (a) was unidimensional but had some unique items, (b) had highly correlated factors, or (c) had a general factor as well as a group factor. In addition, R-PA tended to outperform T-PA if items had higher factor loadings and sample size was large. A major disadvantage of the T-PA method was that it frequently yielded inflated Type I error rates.