Upper panel: example of an EBL shape excluded by Mkn 501 with the VHEConcavity criterion. Lower panel: the spectra of Mkn 501 and Mkn 421 corrected with this particular EBL shape. The flux of the latter is scaled by 10^-3 for better visibility. For Mkn 501, a double broken power law provides the best description with a spectral index Γ₃ =  −35 at highest energies, the maximum value tested in the fitting procedure. In the case of Mkn 421, a simple power law suffices.