The Eliashberg theory of superconductivity is revised in this work. As a result, a new efficient approach for describing the phonon-driven superconductivity is developed, in which the dependence on a traditional empirical parameter responsible for the effect of the Coulomb interaction is completely eliminated. Instead, the screened Coulomb interaction computed fully ab-initio is plugged into equations within its entire energy range. This method allows for reliable predictions of critial temperatures (Tc) of conventional superconductors within the static limit of the screened Coulomb interaction. In the full dynamical case, however, the overstimation of Tc is systematically obtained, which is attributed to, most likely, the lowest-order self-energy approximation. And finally, a new approximation based on elements of Density Functional Theory for Superconductors (SCDFT) is introduced. This allows to reduce the error in the dynamical case and improve over static result.