The short-wavelength-prime (SWP) detector of the International Ultraviolet Explorer should operate near the photon-counting limit, but the noise levels in flat-field images are several times higher. The exaggerated noise can be traced to the incomplete removal of the pixel-to-pixel granularity of the television frames by the prevailing Spectral Image Processing System. An empirical noise model for the current-epoch photometric linearization strategy and one for a hypothetical processing system that achieves complete flat fielding of the raw images are derived. A formula is then proposed to predict the signal-to-noise ratio in the measured flux of an emission line-possibly superimposed on a smooth continuum-in an IUE low-dispersion (5 angstrom resolution) far-ultraviolet (1150 angstrom-1950 angstrom) spectrum as recorded with the SWP camera. For illustration, I specialize the formula to the important C IV-lambda-1549 feature of F-K stars. The S/N relation permits one to determine sensitivity limits, upper limits in faint exposures, and optimum exposure times.