A new version of the Compressible Packing Model (CPM) (de Larrard et al.), the 4-parameter CPM, is introduced to predict the packing density of maximally dense disordered packings of bidisperse spherical particles. Based on the assumption of a dominant granular class, it takes into account the packing process efficiency and two geometrical interactions objects of a new theory: the wall effect and the loosening effect. For the latter, a critical cavity size ratio, below which a fine bead can be inserted into a small cavity created by touching coarser particles, is introduced. When the packing process is perfect, the packing density reaches a maximum virtual density defined as the maximum packing density attainable for a given mixture. In this reference frame, the theory for wall effect and loosening effect is based on a specific treatment of configurations of one secondary class particle surrounded by dominant class neighbours. The four parameters are: the wall effect and the loosening effect coefficients, the compaction index and the critical cavity size ratio which can be adjusted for aggregates, but whose value is 02 for spheres, in harmony with the tetrahedral cavern theory. The 4-parameter CPM demonstrates its efficiency to predict packing density of binary mixtures from the analysis of 320 results. Correlation coefficients are 99% for glass beads (300 values) and 98.7% for numerically simulated spherical particles (20 values). (C) 2016 Elsevier B.V. All rights reserved.