Gal repressosome assembly and repression of the gal operon in Escherichia coli occurs when two dimeric GalR proteins and the histone-like HU protein bind to cognate sites causing DNA looping. Structure-based genetic analysis defined the GalR surfaces interacting to form a stacked, V-shaped, tetrameric structure. Stereochemical models of the four possible DNA loops compatible with the GalR tetramer configuration were constructed using the sequence-dependent structural parameters of the interoperator DNA and conformation changes caused by GalR and asymmetric HU binding. Evaluation of their DNA elastic energies gave unambiguous preference to a loop structure in which the two gal operators adopt an antiparallel orientation causing undertwisting of DNA.