We take the fact that the prefactor Φ(µ (3) , µ (4) ) successfully removes non-physical features from the third order cumulant spectrum in a realistic condensed phase system as an additional proof of the wide applicability of the dampened cumulant response developed in this work (see Eqn. 16). No details of the underlying system Hamiltonian are needed to obtain the ideal dampening factor Φ, and only non-Gaussian features of the energy gap fluctuations determine this quantity. We have demonstrated that constructing Φ(µ (3) , µ (4) ) from a stochastic sampling of simple, exactly solvable model systems provides a recipe for improving cumulant spectra truncated at low order in complex condensed phase systems.