Proof of concept: Comparison between the best fit to the spectrum of Her X-1, obtained with the new fitting approach (solid lines in the upper panel and red residuals in the bottom panel) and the fit performed by Wolff et al. (2016) (dashed lines in the upper panel and blue residuals in the bottom panel). The red component corresponds to Comptonized bremsstrahlung, the orange one to Comptonized cyclotron emission, the violet one to the Comptonized blackbody emission, and the blue one to the iron line complex. The corresponding parameter values are shown in Tab. B.1.