An important distinction is frequently made between constitutively expressed housekeeping genes versus regulated genes. Although generally characterized by different DNA elements, chromatin architecture and cofactors, it is not known to what degree promoter classes strictly follow regulatability rules and which molecular mechanisms dictate such differences. We show that SAGA‐dominated/TATA‐box promoters are more responsive to changes in the amount of activator, even compared to TFIID/TATA‐like promoters that depend on the same activator Hsf1. Regulatability is therefore an inherent property of promoter class. Further analyses show that SAGA/TATA‐box promoters are more dynamic because TATA‐binding protein recruitment through SAGA is susceptible to removal by Mot1. In addition, the nucleosome configuration upon activator depletion shifts on SAGA/TATA‐box promoters and seems less amenable to preinitiation complex formation. The results explain the fundamental difference between housekeeping and regulatable genes, revealing an additional facet of combinatorial control: an activator can elicit a different response dependent on core promoter class. Synopsis Responsiveness, a property that distinguishes housekeeping from regulatable genes, is inherent to core promoter class rather than to activator use. The molecular mechanisms underlying regulatability include various types of negative regulation. Molecular mechanisms at DNA sequence level distinguish housekeeping genes from regulatable genes. Responsiveness is inherent to the core promoter type. SAGA‐dominated/TATA‐like promoters are more responsive to activator presence. Increased activator response is due to TBP removal by Mot1 and nucleosome repositioning. The different level of responsiveness seen for housekeeping vs. regulatable gene promoters is inherent to the underlying DNA sequence rather than to specific activator use.