In a previous study, semiclassically optimized complex absorbing potentials (CAPs) of polynomial form was proposed. It was demonstrated that these potentials can greatly decrease the CPU cost of resonance and scattering calculations in exact quantum dynamical contexts. In the present work, a Stokes analysis is used to complete the justification of the previously proposed optimization method. Based on improvements made to the method, new polynomial CAPs which are much more efficient than even those of the previous study are constructed. The new CAPs are proposed for general use with any type of quantum calculation in the continuum.