Oxygen, nitrogen, and carbon K-shell photoabsorption and photoionization cross sections have been calculated within core-valence-separated coupled cluster (CC) linear response theory for a number of molecular systems, namely, water, ammonia, ethylene, carbon dioxide, acetaldehyde, furan, and pyrrole. The cross sections below and above the K-edge core ionization thresholds were obtained, on the same footing, from L2 basis set calculations of the discrete electronic pseudospectrum yielded by an asymmetric-Lanczos-based formulation of CC linear response theory at the CC singles and doubles (CCSD) and CC singles and approximate doubles (CC2) levels. An analytic continuation procedure for both discrete and continuum cross sections as well as a Stieltjes imaging procedure for the photoionization cross section were applied and the results critically compared.