Modular parts for tuning translation are prevalent in prokaryotic synthetic biology but lacking for eukaryotic synthetic biology. Working in Saccharomyces cerevisiae yeast, we here describe how hairpin RNA structures inserted into the 5′ untranslated region (5′UTR) of mRNAs can be used to tune expression levels by 100-fold by inhibiting translation. We determine the relationship between the calculated free energy of folding in the 5′UTR and in vivo protein abundance, and show that this enables rational design of hairpin libraries that give predicted expression outputs. Our approach is modular, working with different promoters and protein coding sequences, and outperforms promoter mutation as a way to predictably generate a library where a protein is induced to express at a range of different levels. With this new tool, computational RNA sequence design can be used to predictably fine-tune protein production for genes expressed in yeast.