With only four alternative character states, parallelisms and reversals are expected to occur frequently when using nucleotide characters for phylogenetic inference. Greater available character‐state space has been described as one of the advantages of third codon positions relative to first and second codon positions, as well as amino acids relative to nucleotides. We used simulations to quantify how character‐state space and rate of evolution relate to one another, and how this relationship is affected by differences in: tree topology, branch lengths, rate heterogeneity among sites, probability of change among states, and frequency of character states. Specifically, we examined how inferred tree lengths, consistency and retention indices, and accuracy of phylogenetic inference are affected. Our results indicate that the relatively small increases in the character‐state space evident in empirical data matrices can provide enormous benefits for the accuracy of phylogenetic inference. This advantage may become more pronounced with unequal probabilities of change among states. Although increased character‐state space greatly improved the accuracy of topology inference, improvements in the estimation of the correct tree length were less apparent. Accuracy and inferred tree length improved most when character‐state space increased initially; further increases provided more modest improvements.