As found in our previous work, both second and third order cumulant expansions struggle to replicate higher order vibronic progressions in the Morse spectrum. However, we find that the predicted prefactor Φ removes nonphysical characteristics of the third order spectrum entirely. While the degree of improvement for this anharmonic model is not appreciable in comparison to the harmonic systems studied in Fig. , conditioning through the dampening factor Φ remains an effective way to safeguard against unphysical spectral lineshapes. Furthermore, the ability to apply a prefactor parameterized for harmonic systems to a system which now contains anharmonic PESs supports the hypothesis that the dampening factor is indeed independent of the underlying Hamiltonian of the physical system, and instead depends on the non-Gaussian features of the energy gap fluctu-ations alone. This suggests that the fitted dampening factor Φ(µ (3) , µ (4) ) can be applied to complex condensed phase systems with energy gap fluctuations sampled directly from MD simulations.