In a previous paper [J. Chem. Phys. 118, 17 (2003)], we presented an optimal, pure imaginary complex absorbing potential (CAP) of polynomial form, for use with resonance and scattering calculations. The optimal CAP was derived by minimizing reflection and transmission, and was found to greatly reduce CPU time. In this paper, the previous analysis is extended to more general complex polynomial functional forms, and new CAPs are developed which are even more efficient than those of the previous work, especially for highly accurate calculations. (C) 2003 American Institute of Physics.