1. For faster performance, limit the number of data points. See Materials and Method Section F for suggestions. 2. We strongly discourage superfluous zero padding or apodizing data prior to fitting as these effects will propagate into fitting results. We recommend fitting to data in the original measurement domain. See Materials and Methods section E for more information. 3. When applicable, users should enable a zero-order phase fitting parameter to account for residual phasing errors (see SI section G). The presence of spectrally correlated shot-toshot noise (a.k.a. local-oscillator noise) likely limits the ability to accurately phase data, particularly with the projection slice theorem. Therefore, we do not recommend model fitting for phase distorted apparatuses without prior removal of shot-to-shot noise. 4. Calibrated referencing schemes greatly improve precision of fitting parameters by removing correlated shot-to-shot noise. For example, we found edge-pixel referencing reduced uncertainties by a factor of 10 over unreferenced data. 5. The relative variance across data (e.g. due to non-uniform averaging across different waiting time spectra) should be accounted for using 𝐕𝐕 𝐃𝐃 -𝟏𝟏 . This is straight-forward using our GUI interface. See Material and Methods section B for more information. 6. Fitting happens simultaneously across all spectra, and therefore, consistency is required among factors that affect the magnitude of the nonlinear signal throughout the entire experiment (e.g. constant pump power, constant intensity ratio between probe and local oscillator, consistent normalization factors if non-uniformly averaging along waiting time spectra). 7. For best performance, tune the initial parameters to reasonably match the model and data prior to fitting. Our GUI interface provides real-time update of the lineshape model for comparison with the data across several different plots to greatly help with this process. 8. For best performance, boundary conditions should strike a reasonable balance between narrow enough to avoid too many random restarts and wide enough to avoid boundary stalling. Again, our GUI interface is very helpful here.