Gene expression changes are orchestrated by transcription factors (TFs), which bind to DNA to regulate gene expression. It remains surprisingly difficult to predict basic features of the transcriptional process, including in vivo TF occupancy. Existing thermodynamic models of TF function are often not concordant with experimental measurements, suggesting undiscovered biology. Here, we analyzed one of the most well-studied TFs, the yeast zinc cluster Gal4, constructed a Shea-Ackers thermodynamic model to describe its binding, and compared the results of this model to experimentally measured Gal4p binding in vivo. We found that at many promoters, the model predicted no Gal4p binding, yet substantial binding was observed. These outlier promoters lacked canonical binding motifs, and subsequent investigation revealed Gal4p binds unexpectedly to DNA sequences with high densities of its half site (CGG). We confirmed this novel mode of binding through multiple experimental and computational paradigms; we also found most other zinc cluster TFs we tested frequently utilize this binding mode, at 27% of their targets on average. Together, these results demonstrate a novel mode of binding where zinc clusters, the largest class of TFs in yeast, bind DNA sequences with high densities of half sites.