Background: Eukaryotic mRNAs often contain secondary structures in their untranslated regions that are involved in expression regulation. Whether secondary structures in the protein coding regions are of functional importance remains unclear: laboratory studies suggest stable secondary structures within the protein coding sequence interfere with translation, while several bioinformatic studies indicate stable mRNA structures are more frequent than expected. Results: In contrast to several studies testing for unexpected structural stabilities, I directly compare the selective constraint of sites that differ in their structural importance. I. e. for each nucleotide, I identify whether it is paired with another nucleotide, or unpaired, in the predicted secondary structure. I assume paired sites are more important for the predicted secondary structure than unpaired sites. I look at protein coding yeast sequences and use optimal codons and synonymous substitutions to test for structural constraints. As expected under selection for secondary structures, paired sites experience higher constraint than unpaired sites, i.e. significantly lower numbers of conserved optimal codons and consistently lower numbers of synonymous substitutions. This is true for structures predicted by different algorithms. Conclusion: The results of this study are consistent with purifying selection on mRNA secondary structures in yeast protein coding sequences and suggest their biological importance. One should be aware, however, that accuracy of structure prediction is unknown for mRNAs and interrelated selective forces may contribute as well. Note that if selection pressures alternative to translational selection affect synonymous ( and optimal) codon use, this may lead to under- or over-estimates of selective strength on optimal codon use depending on strength and direction of translational selection.