  The detection of a HeII absorption trough in the spectra of three
high-redshift quasars provides new constraints on the spectral shape of the UV
extragalactic background. The relative strengths of the observed flux
decrements at the rest-frame wavelengths of 1216 and 304 A require a relatively
soft radiation field at 4 ryd compared to 1 ryd. If the ionizing metagalactic
flux is dominated by the integrated light from QSOs, and the HeII reionization
of the universe was completed well before z~3, then the UV/soft X-ray spectrum
of individual quasars at these epochs must, once the cosmological ``filtering''
through material along the line of sight is taken into account, satisfy similar
constraints on the average. We model the propagation of AGN-like ionizing
radiation through the intergalactic medium using CUBA, a numerical code
developed in our prior work. We show that, in order to explain the reported
HeII absorption, any thermal component responsible for the ``soft X-ray
excess'' observed in the spectra of AGNs at z<0.3 must, at z~3, have a typical
temperature >80 eV, and a luminosity not exceeding 20% of that of the ``UV
bump''.
