Confidence distributions have received increasing attention in recent years for statistical inference, specifically for meta-analyses involving rare events. Tian et al.  proposed one application of confidence distributions for meta-analyses that involves combining confidence intervals, which have been shown to be a confidence distribution. Another approach by Liu et al.  combines p-value functions, which are a type of confidence distribution. Additionally, an extension of Fisher's p-value combination method is a confidence distribution. While several confidence distribution methods exist, no comparisons have been made to determine which method is best suited for meta-analyses with rare events or heterogeneity. This article compares the performance of these three confidence distribution approaches. We also propose and compare modifications of these three methods to better handle situations with rare events or heterogeneity.