We describe the compression of a water-soluble polymer brush which undergoes compression-induced phase transitions. The solution behavior of the polymer comprising the brush is described using the de Gennes "n-cluster" model which predicts a region of coexistence between dense and dilute phases. We show that compression of the brush can induce the formation of a dense coexisting phase or the elimination of a dilute phase. These compression-induced transitions give rise to discontinuites in compression force profiles, which can be measured experimentally using the surface force apparatus or the atomic force microscope.