The 4-parameter Compressible Packing Model (CPM) has been developed to predict the packing density of binary mixtures of spherical particles. The four parameters are: the loosening effect parameter a, the wall effect parameter b, the compaction index K and a critical cavity size ratio x(o). The two geometrical interactions have been studied theoretically on the basis of a spherical cell centered on a secondary class bead. For the loosening effect, the critical cavity size ratio xo, below which a fine particle can be inserted into a small cavity created by touching coarser particles, is introduced. This is the only parameter which requires adaptation to extend the model to crushed aggregate particles. The 4-parameter CPM proves its efficiency from the analysis of 334 results published in the literature: correlation coefficient is 96.6% and mean absolute deviation is 0.009. By comparison with the original CPM (with a, b, K incorporated) and the 3-parameter model (with a, b and wedging effect parameter c), it is the most accurate and widely applicable. It opens industrial perspectives in high performance concrete, roller-compacted concrete for dams and road construction layers. (C) 2017 Elsevier B.V. All rights reserved.