The hyperfine structure on the levels of the Na ₂ 1 ³Δ _g state reported in Liu et al. [J. Chem. Phys. 115, 3647 (2001)] is analyzed using a new approach that overcomes most of the approximations adopted in the cited article. We exclude an approximation of the united atom, implying that the electron cloud only interacts with the total nuclear spin, and replace it with the interactions between individual nuclei and electrons. Rather than equating the observed intensities in the spectra with the populations of the hyperfine (HF) components of a 1 ³Δ _g state level excited from a hypothetical equilibrium HF ensemble in a state b ³Π _1u, we consider the more realistic excitation-de-excitation schemes in their entirety, and take into account the mixed character of the window levels of the A1Σu+∼b3ΠΩu system, which generally contains fractions of all Ω = 0, 1, 2. We also avoid an approximation of the major component, in which the probabilities of the optical dipole transitions are computed from the 0-th order state vector alone, and compute the contributions from all components of the blended states. The underlying theory and algorithms are described, and the parameters of the new model are fitted and reported.