The contact line of a volatile liquid on a flat substrate is studied theoretically. We show that a remarkable result obtained for a pure-vapour atmosphere (Phys. Rev. E, vol. 87, 2013, 010401) also holds for an isothermal diffusion-limited vapour exchange with air. Namely, for both zero and finite Young’s angles, the motion- and phase-change-related contact-line singularities can in principle be regularised solely by the Kelvin effect (curvature dependence of saturation conditions). The latter prevents the curvature from diverging and rather leads to its versatile self-adjustment. To illustrate the point, the problem is resolved for a distinguished vicinity of the contact line (‘microregion’) in a ‘minimalist’ way, i.e. without any disjoining pressure, precursor film, Navier slip or any other microphysics. This also leads to the determination of the ‘Kelvin-only’ evaporation- and motion-induced apparent contact angles. With the Kelvin-only microscales actually turning out to be quite nanoscopic, other microphysics effects may nonetheless interfere too in reality. The Kelvin-only results will then yield a limiting case within such a more general formulation.