  Choi et al. [Phys. Rev. B 66, 020513 (2002)] recently presented first
principles calculations of the electron-phonon coupling and superconductivity
in MgB2, emphasizing the importance of anisotropy and anharmonicity. We point
out that (1) variation of the superconducting gap inside the sigma- or the
pi-bands can hardly be observed in real samples, and (2) taking the anisotropy
of the Coulomb repulsion into account influences the size of the small gap,
Delta_pi.
