The precise tuning of gene expression levels is essential for the optimal performance of transcriptional regulatory networks. We created 209 variants of the Saccharomyces cerevisiae PHO5 promoter to quantify how different binding sites for the transcription factor Pho4 affect its output. We found that transcription-factor binding affinities determined in vitro could quantitatively predict the output of a complex yeast promoter. Promoter output was precisely tunable by subtle changes in binding-site affinity of less than 3 kcal mol(-1), which are accessible by modifying 1-2 bases. Our results provide insights into how transcription-factor binding sites regulate gene expression, their possible evolution and how they can be used to precisely tune gene expression. More generally, we show that in vitro binding-energy landscapes of transcription factors can precisely predict the output of a native yeast promoter, indicating that quantitative models of transcriptional regulatory networks are feasible.