We present a complete solution of the batch sedimentation process of an initially homogeneous ideal suspension where the Kynch batch flux density function is allowed to have two inflection points. These inflection points can be located in such a way that during the sedimentation process, the bulk suspension is separated from, the supernate by a rarefaction wave or concentration gradient. This observation gives rise to two new modes of sedimentation as qualitative solutions of the batch sedimentation problem that had not been considered in previous studies. A reanalysis of published experimental data indicates that several observed upper concentration gradients can actually be interpreted as a rarefaction wave, and therefore be included in the framework of Kynch's theory. A numerical example shows an upper rarefaction wave in the settling of a flocculated suspension, to which Kynch's theory applies if the solid particles are in hindered settling.