We have produced an evolutionary model for promoters, analogous to the commonly used synonymous/nonsynonymous mutation models for protein-coding sequences. Although our model, called Sunflower, relies on some simple assumptions, it captures enough of the biology of transcription factor action to show clear correlation with other biological features. Sunflower predicts a binding profile of transcription factors to DNA sequences, in which different factors compete for the same potential binding sites. The parametrized model simultaneously estimates a continuous measurement of binding occupancy across the genomic sequence for each factor. We can then introduce a localized mutation, rerun the binding model, and record the difference in binding profiles. A single mutation can alter interactions both upstream and downstream of its position due to potential overlapping binding sites, and our statistic captures this domino effect. Over evolutionary time, we observe a clear excess of low-scoring mutations fixed in promoters, consistent with most changes being neutral. However, this is not consistent across all promoters, and some promoters show more rapid divergence. This divergence often occurs in the presence of relatively constant protein-coding divergence. Interestingly, different classes of promoters show different sensitivity to mutations, with phosphorylation-related genes having promoters inherently more sensitive to mutations than immune genes. Although there have previously been a number of models attempting to handle transcription factor binding, Sunflower provides a richer biological model, incorporating weak binding sites and the possibility of competition. The results show the first clear correlations between such a model and evolutionary processes.