Propagation of error difficulties aside, fitting dephasing parameters to the linear absorption spectrum is severely ill-conditioned even with the constraints afforded by the CLS method. Figure shows VIFs (see Material and Methods section D) for three different scenarios. Panel (A) is for naively fitting to the upper 80% of the linear absorbance spectrum with a linear response model that includes an amplitude (A01), all five dephasing parameters (T Hom -1 , τ 1 , Δ 1 2 , τ 2 , Δ 2 2 ), and a constant offset (c), which is a scenario that is well known to yield poorly constrained fitting parameters. The resulting VIFs range between 10 8 and 10 12 . As an example, consider the result of Δ 1 2 with a VIF of 10 12 which is the inflation that is expected in the variance of Δ 1 2 because one, or more, covariances exist between Δ 1 2 and other fitting variables. If the other six parameters were held constant while fitting Δ 1 2 , then the uncertainty of Δ 1 2 should decrease by a factor of 1,000,000 (i.e. √10 ). In this scenario, the uncertainty of every parameter is so large that any tiny perturbation in the noise causes massive fluctuations in values of the fitting parameters. These results clearly demonstrate that naively fitting all dephasing parameters to the linear absorbance spectrum is an ill-conditioned problem, consistent with prior expectations. Panel (B) shows results for fitting to the upper 80% of the linear absorbance spectrum using constraints on the time constants similar to what is done in the CLS method. Here we consider the cases where the Kubo time constants are known with absolute certainty (squares) or 10% uncertainty (circles). For the more realistic case of uncertain time constants, VIFs range between 10 9 and ~10 , which imply roughly ~100,000× inflation in the uncertainties of Kubo amplitudes and homogeneous dephasing, give or take an order of magnitude. This result explains the large variance seen in panel (A) of Figure , and the necessity of simulating data with a 600:1 SNR in the 2D IR spectra to obtain reliable results for the CLS method. VIFs differ by four to five orders of magnitude between absolutely certain and uncertain Kubo time constants, which implies error bars on Kubo amplitudes and homogeneous dephasing are underestimated by two orders of magnitude. Indeed, this result is observed for the CLS method in Figure (B) and Video S2. Finally, panel (C) shows VIFs for model fitting to the 2D IR waiting-time series. For nondephasing parameters, including the vibrational lifetime, all VIFs are less than 10, meaning multicollinearity is negligible for these parameters. On the other hand, VIFs range between 100 and 3,000 for the remaining dephasing parameters, implying inflated uncertainties between 30× to 50×. Though significant, the inflation of uncertainties in Kubo amplitudes and homogeneous dephasing remains two to four orders of magnitude smaller than for the CLS method.