The sequence of a stretch of nucleotides affects its propensity for errors during replication and expression. Are proteins encoded by stable or unstable nucleotide sequences? If selection for variability is prevalent, one could expect an excess of unstable sequences. Alternatively, if selection against targets for errors were substantial, an excess of stable sequences would be expected. We screened the genome sequences of different organisms for an important determinant of stability, the presence of mononucleotide repeats. We find that codons are used to encode proteins in a way that avoids the emergence of mononucleotide repeats, and we can attribute this bias to selection rather than a neutral process. This indicates that selection for stability, rather than for the generation of variation, substantially influences how information is encoded in the genome.