Neoaves is the most diverse major avian clade, containing ~95% of avian species, and it underwent an ancient but rapid diversification that has made resolution of relationships at the base of the clade difficult. In fact, Neoaves has been suggested to be a "hard" polytomy that cannot be resolved with any amount of data. However, this conclusion was based on slowly evolving coding sequences and ribosomal RNAs and some recent studies using more rapidly evolving intron sequences have suggested some resolution at the base of Neoaves. To further examine the utility of introns and exons for phylogenetics, we sequenced parts of two unlinked clathrin heavy chain genes (CLTC and CLTCL1). Comparisons of phylogenetic trees based upon individual partitions (i.e. introns and exons), the combined dataset, and published phylogenies using Robinson-Foulds distances (a metric of topological differences) revealed more similarity than expected by chance, suggesting there is structure at the base of Neoaves. We found that introns provided more informative sites, were subject to less homoplasy, and provided better support for well-accepted clades, suggesting that intron evolution is better suited to determining closely-spaced branching events like the base of Neoaves. Furthermore, phylogenetic power analyses indicated that existing molecular datasets for birds are unlikely to provide sufficient phylogenetic information to resolve relationships at the base of Neoaves, especially when comprised of exon or other slowly evolving regions. Although relationships among the orders in Neoaves cannot be definitively established using available data, the base of Neoaves does not appear to represent a hard polytomy. Our analyses suggest that large intron datasets have the best potential to resolve relationships among avian orders and indicate that the utility of intron data for other phylogenetic questions should be examined.