Highly compactible filter cakes respond to pump pressure in an unexpected manner. At relatively low pressures, the filtrate rate reaches a constant, maximum value and does not increase when the pressure increases. Slurries containing large fragile floes with high porosity (biosolids, and wastewater sludge) lead to highly compactible sediments and filter cakes. When the local specific flow resistance α increases more rapidly than the local effective pressure ps (da/dps > 1), the region of supercompactibility has been reached. Methods are presented for estimating the magnitude of the pressure at which the rate approaches its limiting value. The interaction of centrifugal and constant-rate pumps with slurries of highly compactible materials is analyzed in this article. Centrifugal pumps should be chosen so that the pump pressure does not fall in the region where the rate is unaffected by pressure. Constant-rate pumps lead to exceedingly high pressures at very short times.