The expression of most genes is regulated by multiple transcription factors. The interactions between transcription factors produce complex patterns of gene expression that are not always obvious from the arrangement of cis-regulatory elements in a promoter. One critical element of promoters is the TATA box, the docking site for the RNA polymerase holoenzyme. Using a synthetic promoter system coupled to a thermodynamic model of combinatorial regulation, we analyze the effects of different strength TATA boxes on various aspects of combinatorial cis-regulation. The thermodynamic model explains 75% of the variance in gene expression in synthetic promoter libraries with different strength TATA boxes, suggesting that many of the salient aspects of cis-regulation are captured by the model. Our results demonstrate that the effect of changing the TATA box on gene expression is the same for all synthetic promoters regardless of the arrangement of cis-regulatory sites we studied. Our analysis also showed that in our synthetic system the strength of the RNA polymerase-TATA interaction does not alter the combinatorial interactions between transcription factors, or between transcription factors and RNA polymerase. Finally, we show that although stronger TATA boxes increase expression in a predictable fashion, stronger TATA boxes have very little effect on noise in our synthetic promoters, regardless of the arrangement of cis-regulatory sites. Our results support a modular model of promoter function, where cis-regulatory elements can be mixed and matched (programmed) with outcomes on expression that are predictable based on the rules of simple protein-protein and protein-DNA interactions.