A central question concerning data collection strategy for molecular phylogenies has been, is it better to increase the number of characters or the number of taxa sampled to improve the robustness of a phylogeny estimate? A recent simulation study concluded that increasing the number of taxa sampled is preferable to increasing the number of nucleotide characters, if taxa are chosen specifically to break up long branches. We explore this hypothesis by using empirical data from noctuoid moths, one of the largest superfamilies of insects. Separate studies of two nuclear genes, elongation factor-1 alpha (EF-1 alpha) and dopa decarboxylase (DDC), have yielded similar gene trees and high concordance with morphological groupings for 49 exemplar species. However, support levels were quite low for nodes deeper than the subfamily level. We tested the effects on phylogenetic signal of (1) increasing the taxon sampling by nearly 60%, to 77 species, and (2) combining data from the two genes in a single analysis. Surprisingly, the increased taxon sampling, although designed to break up long branches, generated greater disagreement between the two gene data sets and decreased support levels for deeper nodes. We appear to have inadvertently introduced new long branches, and breaking these up may require a yet larger taxon sample. Sampling additional characters (combining data) greatly increased the phylogenetic signal. To contrast the potential effect of combining data from independent genes with collection of the same total number of characters from a single gene, we simulated the latter by bootstrap augmentation of the single-gene data sets. Support levels for combined data were at least as high as those for the bootstrap-augmented data set for DDC and were much higher than those for the augmented EF-1 alpha data set. This supports the view that in obtaining additional sequence data to solve a refractory systematic problem, it is prudent to take them from an independent gene.