The accuracy of coupled-cluster methods for the computation of core-valence correction to atomization energy was assessed. Truncation levels up to CCSDTQP were considered together with (aug-)cc-pwCVnZ (n = D, T, Q, 5) basis sets and three different extrapolation techniques (canonical and flexible Helgaker formula and Riemann zeta function extrapolation). With the exception of CCSD, a more accurate correction can be obtained from a larger basis set using a lower-level coupled-cluster method, and not vice versa. For the CCSD(T) level, it also implies faster computations with modern codes. We also discussed the importance of moving to higher-order or all-electron methods for geometry optimizations. The present study provides the general knowledge needed for the most accurate state-of-the-art computations.