Time-correlated single-photon counting of intercalated ethidium bromide was used to measure the torsion constants of positively supercoiled, relaxed, and negatively supercoiled pBR322 DNA, which range in superhelix density from +0.042 to -0.123. DNA behaves as coupled, nonlinear torsional pendulums under superhelical stress, and the anharmonic term in the Hamiltonian is approximately 15 percent for root-mean-square fluctuations in twist at room temperature. At the level of secondary structure, positively supercoiled DNA is significantly more flexible than negatively supercoiled DNA. These results exclude certain models that account for differential binding affinity of proteins to positively and negatively supercoiled DNA.