This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals, which directly proceeds in terms of the quantities driving the algebraic reduction. The method presented in the first article extends to general complex masses in a systematic way with a few slight adjustments required by the fact that the imaginary parts of these quantities are no longer driven by the Feynman prescription of the propagators but by intricate combinations of imaginary masses, which results in different cases sharing a common structure. As in the case of real masses, it incorporates configurations of kinematics that are more general than those pertaining to physical processes.