The measurement of the compressional rheological parameters for an aggregated particulate suspension is described. The parameters include the compressive yield stress and hindered settling function, describing the extent and rate of dewatering respectively. The variation of these parameters with shear rate and time of shear is also considered in the light of their sensitivity to low shear rates, with particular reference to the case of flocculated particulate suspensions. The latter is seen to be important in the future development of a comprehensive understanding of compressive rheology of aggregated particulate suspensions in industrial applications such as thickening, filtration and centrifugation.