The modeling of pressure filtration of flocculated suspensions using compressional rheology and a knowledge of compressional yield stress P-y(phi) and a hydraulic resistance factor r(phi) (phi is the local volume fraction of solids) is shown to yield an initial solids loading that maximizes the throughput of the filter. The optimal initial height h(0) is such that the filtration time to reach a specified average volume fraction as output equals the handling time for the filter press. The maximum throughput of the press is then examined as a function of the remaining control parameters, the initial solids volume fraction phi(0), and the applied piston pressure Delta P. The dependence of filtration time on phi(0)/phi(infinity) (where phi(infinity) is the volume fraction of solids at infinite time under applied pressure Delta P) enables the construction of a simple numerical model for the pressure filtration process, which accurately approximates predictions of the full compressional rheology model.