The literature contains two forms of the two-nucleon potential computed to fourth order in the coupling constant from, the gradient coupling of the pi-meson to the nucleon field. These are commonly referred to as the Taketani-Machida-Onuma (T. M. O.) and the Brueckner-Watson (B. W.) potentials. The merits of the controversy surrounding this schism are reexamined from first principles starting from the covariant equation for two-nucleons, and it is concluded that the conditions for the applicability of the method leading to the T. M. O. potential are never satisfied in practice. On the other hand, the B. W. potential, suitably altered following recent suggestions by Miyazawa and the author may well yield a suitable approximation in the low energy region.