Benchmark scalar-relativistic core-valence-separated (CVS) equation-of-motion coupled-cluster ionization potential (EOMIP-CC) calculations of 21 K-edge ionization energies of C, O, N, and F in 14 molecules are reported. The CVS-EOMIP-CC methods are shown to be numerically more stable and more accurate than the parent EOMIP-CC methods, even when the calculations using the latter can be tightly converged. The superior performance of the CVS scheme is attributed to the exclusion of spurious couplings between core-ionized states and valence continuum states. Systematic improvement of computed K-edge ionization energies within the CVS-EOMIP-CC hierarchy, including the CC singles and doubles (CCSD) method, the CC singles, doubles, and triples (CCSDT) method, and the CC singles, doubles, triples, and quadruples (CCSDTQ) method, is demonstrated, with CCSDTQ yielding essentially quantitative results. Maximum absolute deviations between computed and experimental results amount to 2.54 eV for CCSD/cc-pCVQZ, 0.54 eV for CCSDT/cc-pCVQZ, and 0.23 eV for CCSDT/cc-pCVQZ augmented with quadruples contributions using the cc-pVTZ basis sets. The corresponding standard deviations are 1.91 eV for CCSD/cc-pCVQZ, 0.18 eV for CCSDT/cc-pCVQZ, and 0.10 eV for CCSDT/cc-pCVQZ augmented with quadruples contributions using the cc-pVTZ basis sets. Finally, CVS-EOMIP-CCSDT/cc-pCVTZ calculations of core ionization energies in CH3CN and CH3NC are reported, and experimental re-investigation of carbon 1s ionization energies in CH3CN is suggested.