The binding of tryptophan repressor (TrpR) to its operators was examined quantitatively using in vitro and in vivo methods. DNA sequence requirements for 1:1 and tandem 2:1 (TrpR:DNA) binding in various sequence contexts were studied. The results indicate that the optimal half-site sequence for recognition by one helix-turn-helix motif of one TrpR dimer is 3'CNTGA5'5'GNACT3', consistent with contacts observed by X-ray diffraction analysis of cocrystalline 1:1 and 2:1 complexes. Half-sites can be paired to form a palindrome either by direct abutment, forming the nucleation site for a tandem 2:1 complex, or with an 8-base-pair spacer, forming a 1:1 target. Dimethylsulfate (DMS) methylation-protection footprinting in vitro of 1:1 and 2:1 complexes formed sequentially on the two unequal half-site pairs of the trpEDCBA operator from Serratia marcescens indicated an obligate hierarchy of site occupancy, with one half-site pair serving as the nucleation site for tandem binding. DMS footprinting of Escherichia coli operators in vivo showed that, over a wide range of intracellular TrpR concentration, the trpEDCBA operator is occupied by three repressor dimers, aroH is occupied by two dimers, and the 1:1 binding mode is used on the trpR operator. The coexistence of these distinct occupancy states implies that changes in protein concentration affect only the fractional occupancy of each operator rather than the binding mode, which is determined by the number of half-site sequences present in the operator region. Cooperativity of tandem complex formation measured by gel retardation using a symmetrized synthetic operator containing identical, optimal sites spaced as in natural operators was found to be modest, implying a maximum coupling free energy of approximately -2 kcal/mol. On other sequences the apparent degree of cooperativity, as well as the apparent affinity, varies with sequence and sequence context in a manner consistent with the structural models and which suggests compensation between affinity and cooperativity as a mechanism that allows tolerance of operator sequence variation.