Top: example spectra from the test on stacking mock samples where all sources had a broad component below the noise levels, for each of the different weights usedd. Also given are the significance values of the excess emission due to a broad component, for each example. Middle: example spectra from the test on stacking mock samples where all sources had no added broad component. Bottom: example spectra from the test on stacking mock samples where all sources had no added broad component, but without using velocity re-binning. We also show the one (red curve) and two-component fits (blue solid and dashed curves) to the stacked lines.