Phylogenetic studies based on molecular sequence alignments are expected to become more accurate as the number of sites in the alignments increases. With the advent of genomic-scale data, where alignments have very large numbers of sites, bootstrap values close to 100% and posterior probabilities close to 1 are the norm, suggesting that the number of sites is now seldom a limiting factor on phylogenetic accuracy. This provokes the question, should we be fussy about the sites we choose to include in a genomic-scale phylogenetic analysis? If some sites contain missing data, ambiguous character states, or gaps, then why not just throw them away before conducting the phylogenetic analysis? Indeed, this is exactly the approach taken in many phylogenetic studies. Here, we present an example where the decision on how to treat sites with missing data is of equal importance to decisions on taxon sampling and model choice, and we introduce a graphical method for illustrating this.