Comparison of the optical emission-line properties of 55 low-redshift (z < 0.5) QSOs with their 2 keV X-ray luminosities has revealed two previously unseen correlations. The asymmetry of the Hbeta profile and the ratio of the emission in the Fe II complex at 4550 angstrom to that in Hbeta are strongly correlated with X-ray luminosity, while correlations between X-ray luminosity and other line parameters, including the Fe II equivalent width, are probable. These correlations do not seem to be attributable to orientation effects and appear to be followed by both radio-loud and radio-quiet objects. Consistent with photoionization models, these results suggest that them exists an X-ray-absorbing region in the broad-line clouds in which Fe II emission arises from collisional excitation. A contribution to the Hbeta emission from collisional excitation in the same region may also explain the Hbeta asymmetry/X-ray luminosity correlation, as well as low Lyalpha/Hbeta intensity ratios. Differences in the X-ray optical depth of the broad-line clouds may thus be the main source of differences in the optical emission-line properties of these objects. If this interpretation is correct, then the new correlations imply an anticorrelation between X-ray luminosity and the mean X-ray optical depth of the broad-line clouds.