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Artifactual evidence of adaptive amino acid substitution can be generated within a McDonald-Kreitman test if some amino acid mutations are slightly deleterious and there has been an increase in effective population size. Here I investigate the conditions under which this occurs. I show that fairly small increases in effective population size can generate artifactual evidence of positive selection if there is no selection upon synonymous codon use. This problem is exacerbated by the removal of low-frequency polymorphisms. However, selection on synonymous codon use restricts the conditions under which artifactual evidence of adaptive evolution is produced.