We inferred phylogenetic trees from individual genes and random samples of nucleotides from the mitochondrial genomes of 10 vertebrates and compared the results to those obtained by analyzing the whole genomes. Individual genes are poor samples in that they infrequently lead to the whole-genome tree. A large number of nucleotide sites is needed to exactly determine the whole-genome tree. A relatively small number of sites, however, often results in a tree close to the whole-genome tree. We found that blocks of contiguous sites were less likely to lead to the whole-genome tree than samples composed of sites drawn individually from throughout the genome. Samples of contiguous sites are not representative of the entire genome, a condition that violates a basic assumption of the bootstrap method as it is applied in phylogenetic studies.