We investigate the relationship between the rest-frame equivalent width (EW) of the C IV λ1549 broad-emission line, monochromatic luminosity at rest-frame 5100 A, and the Hbeta-based Eddington ratio in a sample of 99 ordinary quasars across the widest possible ranges of redshift (0 ~3 σ\ level, by exhibiting C IV lines much weaker than predicted from their Hbeta-based Eddington ratios. Assuming the supermassive black-hole masses in all quasars can be determined reliably using the single-epoch Hbeta-method, our results indicate that EW(C IV) cannot depend solely on the Eddington ratio. We briefly discuss a strategy for further investigation into the roles that basic physical properties play in controlling the relative strengths of broad-emission lines in quasars. ; Comment: 7 pages (emulateapj), 2 figures. Accepted for publication in ApJ