Genome-wide distribution of histone H3K18 and H3K27 acetyltransferases, CBP (CREBBP) and p300 (EP300), is used to map enhancers and promoters, but whether these elements functionally require CBP/p300 remains largely uncertain. Here we compared global CBP recruitment with gene expression in wild-type and CBP/p300 double-knockout (dKO) fibroblasts. ChIP-seq using CBP-null cells as a control revealed nearby CBP recruitment for 20% of constitutively-expressed genes, but surprisingly, three-quarters of these genes were unaffected or slightly activated in dKO cells. Computationally defined enhancer-promoter-units (EPUs) having a CBP peak near the enhancer-like element were more predictive, with CBP/p300 deletion attenuating expression of 40% of such constitutively-expressed genes. Examining signal-responsive (Hypoxia Inducible Factor) genes showed that 97% were within 50 kilobases of an inducible CBP peak, and 70% of these required CBP/p300 for full induction. Unexpectedly, most inducible CBP peaks occurred near signal-nonresponsive genes. Finally, single-cell expression analysis revealed additional context dependence where some signal-responsive genes were not uniformly dependent on CBP/p300 in individual cells. While CBP/p300 was needed for full induction of some genes in single-cells, for other genes CBP/p300 increased the probability of maximal expression. Thus, target gene context influences the transcriptional requirement for CBP/p300, possibly by multiple mechanisms.