The spectral line shapes for the HD rotational spectra perturbed by He and Ar gases, which show interference between allowed and collisionally induced dipole transitions, are calculated including the effects of inelastic rotational collisions. The general parametrization of the line shape, including inelastic collisions, requires six independent real parameters as opposed to four in the theory of Herman, Tipping, and Poll [Phys. Rev. A 20, 2006 (1979)]. Semiclassical calculations based on classical trajectories indicate the importance of the inelastic effects and show qualitative agreement with the experimental parameters. However, it is clear that a fu11 explanation of experimental data will eventua11y require a full quantum treatment.PACS number(s): 32.70.Jz, 32.80. Pj, 34.50.Rk