The compressional rheology of cellulose fibre suspensions has been studied using a pressure filtration technique. The dewatering of these systems is thus described in terms of various key properties of the suspension, including the compressive yield stress, permeability and solids diffusivity, permitting a quantitative characterisation of the consolidation process. We investigate as a particular example the effect of a commercial debonding agent additive on the compressional properties of a fibre suspension. Such agents are commonly used in the production of hygiene products where they are added to decrease the strength of fibre-fibre bonds. Here we investigate their effect on the compressive response of fibre suspensions as an example of how measurements of this type can be used to characterise the effect of additives on bulk properties. The results indicate that addition of debonder causes a somewhat higher dewatering tendency as the solids level is increased.