We measured at high energy and angular resolution the spectral width of photoemission features near the Fermi energy for Ag(100) and for the nearly-two-dimensional metal 2H-NbSe2. The results do not agree with the quadratic width-energy relationship predicted for the lifetime broadening of a Fermi liquid: We found a nearly inverse linear relationship for the sp band of Ag(100), and a similar behavior in the case of NbSe2. These results indicate that the broadening is primarily affected by extrinsic factors rather than by the lifetime-and also that the "anomalous" broadening of the photoemission spectra found for the normal state of the high-temperature superconductors cannot be automatically interpreted as evidence of non-Fermi-liquid behavior.