To characterize and optimize the compressive dewatering of suspensions, rapidly, determinable material parameters are required. A mathematical framework, exists for characterization of dewatering using three parameters: the compressive yield stress P-y(phi), the hindered settling function r(phi), and a solids diffusivity D(phi). A new variation on traditional constant pressure, batch filtration tests is described along with a computer-controlled filtration apparatus that enables complete characterization of a suspension with respect to dewatering in a matter of hours. The testing methods are validated experimentally on flocculated zirconia suspensions along with calculation of the material dewatering parameters. Application of the calculated parameters to modeling of a real filtration test shows excellent agreement. Practical implications of the modeling are also discussed.