Chromatin influences gene expression by restricting access of DNA binding proteins to their cognate sites in the genome. Large-scale characterization of nucleosome positioning in Saccharomyces cerevisiae has revealed a stereotyped promoter organization in which a nucleosome-free region (NFR) is present within several hundred base pairs upstream of the translation start site. Many transcription factors bind within NFRs and nucleate chromatin remodelling events which then expose other cis-regulatory elements. However, it is not clear how transcription-factor binding and chromatin influence quantitative attributes of gene expression. Here we show that nucleosomes function largely to decouple the threshold of induction from dynamic range. With a series of variants of one promoter, we establish that the affinity of exposed binding sites is a primary determinant of the level of physiological stimulus necessary for substantial gene activation, and sites located within nucleosomal regions serve to scale expression once chromatin is remodelled. Furthermore, we find that the S. cerevisiae phosphate response (PHO) pathway exploits these promoter designs to tailor gene expression to different environmental phosphate levels. Our results suggest that the interplay of chromatin and binding-site affinity provides a mechanism for fine-tuning responses to the same cellular state. Moreover, these findings may be a starting point for more detailed models of eukaryotic transcriptional control.