The compressive yield stress, P-y(phi), is an important rheological parameter for the characterization of concentrated flocculated suspensions. It is a measure of the compressive strength of interparticle bonds in a strongly networked suspension structure and is used in the design of processes for the dewatering of fine particle suspensions. There are several techniques available to determine the compression characteristics of a particular suspension. Three techniques are described and compared : two based on centrifugal consolidation and one based on pressure filtration. Results for well-characterized ZrO2 and Al2O3 suspension systems are presented, showing the effect of flocculation conditions, sample preparation methods, and the initial suspension concentration on the compression rheology. The application of these findings to the design of a compression thickener for the concentration of bauxite residue or red mud for semidry disposal in the alumina industry is also explained.