The aim of this paper is to fully determine the parameters of the approximate homogenized yield criterion for porous ductile solids containing arbitrary ellipsoidal cavities proposed in Part I. This is done through improvements of the limit-analysis of some representative hollow cell presented there. The improvements are of two kinds. For hydrostatic loadings, the limit-analysis is refined by performing micromechanical finite element computations in a number of significant cases, so as to replace Leblond and Gologanu (2008)'s trial velocity field representing the expansion of the void by the exact, numerically determined one. For deviatoric loadings, limit-analysis is dropped and direct use is made of some general rigorous results for nonlinear composites derived by Ponte-Castaneda (1991), Willis (1991) and Michel and Suquet (1992) using the earlier work of Willis (1977) and the concept of " linear comparison material ". This hybrid approach is thought to lead to the best possible expressions of the yield criterion parameters. The criterion proposed reduces to (variants of) classical approximate criteria proposed by Gurson (1977) and Gologanu et al. (1993, 1994, 1997) in the specific cases of spherical or spheroidal, prolate or oblate cavities. An overview of the validation of this criterion through micromechanical finite element computations is finally presented.