We present three new absolutely calibrated continuous stellar spectra from 3 to 35um, constructed as far as possible from actual observed spectral fragments taken from the Kuiper Airborne Observatory (KAO), and the IRAS Low Resolution Spectrometer (LRS). These stars - alpha1 Cen, alpha TrA, and epsilon Car - augment our previous archive of complete absolutely calibrated spectra for northern K and M giants. All these spectra have a common calibration pedigree. The wavelength coverage is ideal for calibration of many existing and proposed ground-based, airborne, and satellite sensors. KAO and IRAS data in the 15-30 um range suggest that the spectra of cool giants are close to Rayleigh-Jeans slopes. Our observations of alpha1 Cen, absolutely calibrated via our adopted Sirius model, indicate an angular diameter in very good agreement with values in the literature, demonstrating "closure" of the set of spectra within our absolute framework. We compare our observed alpha1 Cen spectrum with a published grid of theoretical models from Kurucz, and adopt a plausible theoretical shape, that fits our spectrum, as a secondary reference spectrum in the southern sky.