NRLEUV represents an independent approach to modeling the Sun's EUV irradiance and its variability. Our model utilizes differential emission measure distributions derived from spatially and spectrally resolved solar observations, full-disk solar images, and a database of atomic physics parameters to calculate the solar EUV irradiance. In this paper we present a new solar minimum irradiance spectrum for wavelengths below 1200 Å. This spectrum is based on extensive observations of the quiet Sun taken with the CDS and SUMER spectrometers on the Solar and Heliospheric Observatory (SOHO) and the most recent version of the CHIANTI atomic physics database. In general, we find excellent agreement between this new irradiance spectrum and our previous quiet-Sun reference spectrum derived primarily from Harvard Skylab observations. Our analysis does show that the quiet-Sun emission measure above about 1 MK declines more rapidly than in our earlier emission measure distribution and that the intensities of the EUV free-bound continua at some wavelengths are somewhat smaller than indicated by the Harvard observations. Our new reference spectrum is also generally consistent with recent irradiance observations taken near solar minimum. There are, however, two areas of persistent disagreement. Our solar spectrum indicates that the irradiance measurements overestimate the contribution of the EUV free-bound continua at some wavelengths by as much as a factor of 10. Our model also cannot reproduce the observed irradiances at wavelengths below about 150 Å. Comparisons with spectrally resolved solar and stellar observations indicate that only a small fraction of the emission lines in the 60-120 Å wavelength range are accounted for in CHIANTI.