We have recently devoted two reports to the very weak absorption spectrum of water vapor in the 12,969 – 13,417 cm-1 region by high sensitivity cavity ring down spectroscopy (CRDS) [Vasilchenko et al. J. Quant. Spectrosc. Radiat. Transfer 275 (2021) 107,847; doi.org/10.1016/j.jqsrt.2021.107847; Vasilchenko et al. Molecular Physics e2051762; doi.org/10.1080/00,268,976.2022.2051762]. This spectral interval is important because it includes the region of the oxygen A-band near 760 nm. The achieved sensitivity allowed us to measure lines with intensity on the order of 10–29 cm molecule-1, about two orders of magnitude lower than the detectivity threshold of previous studies. A total of about 240 energy levels of H216O were newly determined. Our comparison to the W2020 empirical levels [Furtenbacher et al. J. Phys. Chem. Ref. Data 49 (2020) 043,103; doi.org/10.1063/5.0030680] led us to identify and correct about 300 W2020 energy levels of the main isotopologue differing from our energy value by more than 5 × 10–3 cm-1. In the present contribution, we consider in details the sources of the W2020 energy levels to identify the origin of these deviations. We confirm that more than 260 energy levels should be corrected but for the remaining thirty-two levels, the W2020 energy values are in fact, more reliable. As a result, we propose an improved list of energy levels retrieved from the CRDS data and a recommended line list for water vapor in natural isotopic abundance in the 12,969 – 13,417 cm-1 region, mostly based on the CRDS line parameters.