The results in Fig. are obtained for a harmonic model system. In this work, we argue that 1) the general functional form of Eqn. 16 provides a pathway of improving cumulant lineshapes even in realistic systems with more complex (generally anharmonic) potential energy surfaces as encountered in condensed phase systems sampled with MD; and that 2) the optimal dampening factor Φ can be expressed as a function of the non-Gaussian features of the underlying energy gap fluctuations, such that Φ ≡ Φ µ (3) , µ (4) .