We propose a new approach for deriving the solar irradiance due to the emission by solar upper atmosphere plasmas at 2 × 10⁴ ≤ T ≤ 2 × 10⁷ K for wavelengths shorter than 800 Å. Our approach is based on a new understanding of the properties of the solar upper atmosphere; specifically, the discovery that the majority of emission from the nonflaring solar upper transition region and corona in the temperature range 3 × 10⁵ ≤ T ≤ 3 × 10⁶ K arises from isothermal plasmas that have four distinct temperatures: 0.35, 0.9, 1.4, and 3 × 10⁶ K. Although the lower transition region (2 × 10⁴ ≤ T ≤ 2 × 10⁵ K) of coronal holes, quiet regions or active regions, is multithermal and variable in brightness, the shape of emission measure versus temperature curves in this region is almost constant. At any given time, flaring plasmas are for the most part isothermal, although their emission measure and temperature continuously change. In this paper we review these recent results and propose a set of simple spectrometers for recording the solar spectrum in several narrow bands. The solar emission measure, average plasma temperature, and composition can be derived using the measured line fluxes. By combining the emission measure and other plasma properties with the output of a suite of atomic physics codes, which are also described here, the solar irradiance at wavelengths shorter than 800 Å can be calculated.