[en] The phase boundary between normal and superconducting phases of the negative-U Hubbard model is obtained within a self-consistent weak-coupling approach known as the ''pseudopotential parquet'' approximation. The shortcomings of simpler self-consistent approaches, including the Hartree-Fock and fluctuation-exchange approximations, are outlined. For intermediate values of U, pseudopotential parquet predicts (i) a maximum in the superconducting transition temperature T_c at an electron filling left-angle n right-angle of approximately 0.92; and (ii) a sharp decrease in T_c for values of left-angle n right-angle closer to 1. The scale of transition temperatures is consistent with results from quantum simulations