Many phylogenetic analyses that include numerous terminals but few genes show high resolution and branch support for relatively recently diverged clades, but lack of resolution and/or support for "basal" clades of the tree. The various benefits of increased taxon and character sampling have been widely discussed in the literature, albeit primarily based on simulations rather than empirical data. In this study, we used a well-sampled gene-tree analysis (based on 100 mitochondrial genomes of higher teleost fishes) to test empirically the efficiency of different methods of data sampling and phylogenetic inference to "correctly" resolve the basal clades of a tree (based on congruence with the reference tree constructed using all 100 taxa and 7990 characters). By itself, increased character sampling was an inefficient method by which to decrease the likelihood of "incorrect" resolution (i.e., incongruence with the reference tree) for parsimony analyses. Although increased taxon sampling was a powerful approach to alleviate "incorrect" resolution for parsimony analyses, it had the general effect of increasing the number of, and support for, "incorrectly" resolved clades in the Bayesian analyses. For both the parsimony and Bayesian analyses, increased taxon sampling, by itself, was insufficient to help resolve the basal clades, making this sampling strategy ineffective for that purpose. For this empirical study, the most efficient of the six approaches considered to resolve the basal clades when adding nucleotides to a dataset that consists of a single gene sampled for a small, but representative, number of taxa, is to increase character sampling and analyze the characters using the Bayesian method.