With continuously improving signal-to-noise ratios, a statistically sound analysis of quasi-elastic neutron scattering (QENS) spectra requires to fit increasingly complex models which poses several challenges. Simultaneous fits of the spectra for all recorded values of the momentum transfer become a standard approach. Spectrometers at spallation sources can have a complicated non-Gaussian resolution function which has to be described most accurately. At the same time, to speed up the fitting, an analytical convolution with this resolution function is of interest. Here, we discuss basic concepts to efficient approaches for fits of QENS spectra based on standard MATLAB and Python fit algorithms. We illustrate the fits with example data from IN16B, BASIS, and BATS.