When a cell's environment changes, a large transcriptional response often takes place. The exquisite sensitivity and specificity of these responses are controlled in large part by the combinations of cis-regulatory elements that reside in gene promoters and adjacent control regions. Here, we present a study aimed at accurately modeling the relationship between combinations of cis-regulatory elements and the expression levels they drive in different environments. We constructed four libraries of synthetic promoters in yeast, consisting of combinations of transcription factor binding sites and assayed their expression in four different environments. Thermodynamic models relating promoter sequences to their corresponding four expression levels explained at least 56% of the variation in expression in each library through the different conditions. Analyses of these models suggested that a large fraction of regulated gene expression is explained by changes in the effective concentration of sequence-specific transcription factors, and we show that in most cases, the corresponding transcription factors are expressed in a pattern that is predicted by the thermodynamic models. Our analysis uncovered two binding sites that switch from activators to repressors in different environmental conditions. In both the cases, the switch was not the result of a single transcription factor changing regulatory modes, but most likely due to competition between multiple factors binding to the same site. Our analysis suggests that this mode of regulation allows for large and steep changes in expression in response to changing transcription factor concentrations. Our results demonstrate that many complex changes in gene expression are accurately explained by simple changes in the effective concentrations of transcription factors.