The paper by Nold et al. [Phys. Fluids, 26, 072001 (2014)] examined density profiles and the micro-scale structure of an equilibrium three-phase (liquid-vapour-solid) contact line in the immediate vicinity of the wall using elements from the statistical mechanics of classical fluids, namely density-functional theory. The present research note, building on the above work, further contributes to our understanding of the micro-scale structure of a contact line by quantifying the strong dependence of the liquid-vapour density profile on the normal distance to the interface, as compared to the dependence on the vertical distance to the substrate. A recent study by Benet et al. [J. Phys. Chem. C, 22079 (2014)] has shown that this could explain the emergence of a film-height dependent surface tension close to the wall, with implications for the Frumkin-Derjaguin theory.