Population studies of faint X-ray sources (e.g. galaxies, AGN, $\gamma$-ray bursts and their afterglows) have become more and more common. The problem of obtaining an average spectrum in the rest-frame of the sources is non-trivial. We show that conventional methods for averaging low signal-to-noise X-ray spectra, when applied to sources at different redshifts, result in a mean rest-frame spectrum that can exhibit artificial features. These include the broadening and weakening of emission/absorption lines, a broad dip in the continuum above an emission line, and a spectral hardening at the highest energies. All of these effects have been observed in real data and have been given fairly weighty astrophysical and/or cosmological interpretations. We present a new method of averaging which considerably reduces the severity of the problems.