The measured effective torsional rigidities of Single twisted DNAs under Various tensions conflict with theoretical predictions of Motoz and Nelson.(MN) At low forces in the 0.275-2.0 pN range. However, MN theory was recently shown to agree well With effective torsional rigidities obtained,from simulations, indicating that MN theory is valid down to 0.25 pN for a filament with a constant intrinsic torsional rigidity. Her MN theory is used with an assumed persistence, length, 50 mn, to. obtain the force-dependent, intrinsic torsional: rigidity of the filament at each force from its measured effective torsional rigidity. The resulting values rise similar to 1.8-fold with increasing fore from 0.25 to 2.0 pN. Unexpected behavior of the relative extensions of the Untwisted DNAs of Mosconi et al. is noted, and ascribed to a small increase in contour length with force over the 0.18-2.0 pN range. The:variations of both the intrinsic torsional rigidity and rise per base pair (bp) with force are suggested to arise from a force-induced shift Of a cooperative,equilibrium between two conformations with different rises per bp. A two-state nearest-neighbor model is formulated, and ranges of optimal parameters are determined by fitting the model to the experimental differences in rise per bp as a function of force. Optimal adjustment of the torsion elastic constants of the two states enables the same optimal model(s) with fixed, parameters to provide reasonably good fits, of the experimental torsion elastic constant data The results reconcile single-molecule measurements on DNAs under tension with numerous results from fluorescence polarization anisotropy, topoisomer distributions, X-ray scattering of DNAs with attached gold colloids, and other kinds of measurements.