Cis-regulatory elements (CREs) control gene expression by recruiting transcription factors (TFs) and other DNA binding proteins. We aim to understand how individual nucleotides contribute to the function of CREs. Here we introduce CRE analysis by sequencing (CRE-seq), a high-throughput method for producing and testing large numbers of reporter genes in mammalian cells. We used CRE-seq to assay >1,000 single and double nucleotide mutations in a 52-bp CRE in the Rhodopsin promoter that drives strong and specific expression in mammalian photoreceptors. We find that this particular CRE is remarkably complex. The majority (86%) of single nucleotide substitutions in this sequence exert significant effects on regulatory activity. Although changes in the affinity of known TF binding sites explain some of these expression changes, we present evidence for complex phenomena, including binding site turnover and TF competition. Analysis of double mutants revealed complex, nucleotide-specific interactions between residues in different TF binding sites. We conclude that some mammalian CREs are finely tuned by evolution and function through complex, nonadditive interactions between bound TFs. CRE-seq will be an important tool to uncover the rules that govern these interactions.