The impact of synonymous codon choice on protein output has important implications for understanding endogenous gene expression and design of synthetic mRNAs. Previously, we used a neural network model to design a series of synonymous fluorescent reporters whose protein output in yeast spanned a seven-fold range corresponding to their predicted translation speed. Here, we show that this effect is not due primarily to the established impact of slow elongation on mRNA stability, but rather, that an active mechanism further decreases the number of proteins made per mRNA. We combine simulations and careful experiments on fluorescent reporters to argue that translation initiation is limited on non-optimally encoded transcripts. Using a genome-wide CRISPRi screen to discover factors modulating the output from non-optimal transcripts, we identify a set of translation initiation factors including multiple subunits of eIF3 whose depletion restored protein output of a non-optimal reporter. Our results show that codon usage can directly limit protein production, across the full range of endogenous variability in codon usage, by limiting translation initiation.