The method includes the following steps: (i) feeding a slurry into the inlet of a press; (ii) removing liquid from the slurry as the slurry advances through a deliquefying section of the press, thereby producing a pressate stream; (iii) forming a plug of material as the slurry is advanced through a plug formation section of the press; (iv) advancing the plug of material to a discharge section of the press; and (v) removing additional liquid from the plug of material by operating the press so that the pressure in the discharge section of the press is greater than the pressure of the pressate stream by at least 2 psi. There is also described a method for controlling discharge consistency from a press, without provision of discharge restrictors, by varying a pressure differential between a discharge section of the press and a pressate stream.