Topoisomer distributions created by the action of topoisomerase I on p30 delta DNA in the presence of various concentrations of ethidium are measured and analyzed using recently developed theory to obtain the twist energy parameter (ET) that governs the free energy of supercoiling in each case. Competitive dialysis experiments to investigate the relative affinity of ethidium for linear and supercoiled DNAs at different binding ratios are assayed fluorometrically and the results are analyzed using related theory. The topoisomer distributions and fluorescence intensity ratios agree well with the theory, which is based on the assumption that the supercoiling free energy varies quadratically with the effective linking difference, regardless of ethidium binding or superhelix density. The topoisomer distribution experiments alone yield an average best-fit value, ET = 950 +/- 80, independent of ethidium binding ratio from r = 0 to 0.082, while the combined topoisomer distribution and ethidium binding experiments yield an average best-fit value, ET = 1030 +/- 90, which is essentially independent of ethidium binding ratio from r = 0 to 0.082 and superhelix density from sigma = 0 to (-)0.053. One may conclude that the supercoiling free-energy-varies quadratically with effective linking difference over the entire range of observed ethidium binding ratios and superhelix densities. The independently measured torsion constant (alpha) of p30 delta DNA is likewise essentially independent of superhelix density and ethidium binding ratio. The observed invariance of ET and alpha implies that the bending constant kappa beta is similarly invariant to superhelix density and ethidium binding ratio. The apparently ideal behavior displayed by p30 delta DNA is not exhibited by pBR322 DNA, which is discussed in the following companion paper.