In a recent paper [Velichko TI, Mikhailenko SN, Tashkun SA, Global multi-isotopologue fit of measured rotation and vibration–rotation line positions of CO in X 1 Σ + state and new set of mass-independent Dunham coefficients. J Quant Spectrosc Radiat 2012;113:1643–55], mass-independent Dunham coefficients were determined in a global fit of all available pure rotational and vibrational–rotational spectroscopic data for seven isotopologues of the ground X 1 Σ + electronic state of carbon monoxide. Comparisons were made with previous sets of molecular constants, including the quantum-mechanical constants obtained in 2004 [Coxon JA, Hajigeorgiou PG. Direct potential fit analysis of the X 1 Σ + ground state of CO. J Chem Phys 2004;121:2992–3008]. Velichko et al. reported apparent large errors in spectroscopic line positions calculated from the set of constants of Coxon and Hajigeorgiou. It is shown here that the calculations of Velichko et al. are incorrect and that the molecular constants reported by Coxon and Hajigeorgiou are accurate and reproduce all relevant spectroscopic line positions to the same degree of precision as that achieved in the direct potential fit analysis.