Model fitting to the nonlinear waiting-time-dependent spectra provides a natural solution to these issues. Directly fitting the data to a user-supplied lineshape model does not depend on the short-time approximation. It allows users to match the time/frequency domain(s) in which they collect data, and thereby mitigate apodization bias. It does not depend on fitting the linear absorption spectrum, and therefore, enables accurate measurements of spectral diffusion in a variety of scenarios that were previously inaccessible. Finally, as we will show, model fitting is reliable at far lower SNR (e.g. 10:1), is far less susceptible to structured residual signals than the CLS method, and yields reliable uncertainties for the measured lineshape parameters.