The theory of Black and Delgarno that the relative populations of the excited rotational levels of H2 can be understood in terms of cascading following absorption in the Lyman and Werner bands is employed to infer the gas densities and radiation fields within diffuse interstellar clouds containing H2 that is optically thin in those bands. The procedure is described for computing the populations of the different rotation levels, the relative distribution among the different rotation levels of newly formed H2 is determined on the basis of five simplified models, and the rate of H2 formation is estimated. The results are applied to delta Ori, two components of iota Ori, the second components of rho Leo and zeta Ori, tau Sco, gamma Vel, and zeta Pup. The inferred parameters are summarized for each cloud.