The purpose of this work is to systematically study the effect of the throat and the pore sizes on the sound absorbing properties of open-cell foams. The three-dimensional idealized unit cell used in this work enables to mimic the acoustical macro-behavior of a large class of cellular solid foams. This study is carried out for a normal incidence and also for a diffuse field excitation, with a relatively large range of sample thicknesses. The transport and sound absorbing properties are numerically studied as a function of the throat size, the pore size, and the sample thickness. The resulting diagrams show the ranges of the specific throat sizes and pore sizes where the sound absorption grading is maximized due to the pore morphology as a function of the sample thickness, and how it correlates with the corresponding transport parameters. These charts demonstrate, together with typical examples, how the morphological characteristics of foam could be modified in order to increase the visco-thermal dissipation effects.