Two empirical flux laws, one continuous and one discontinuous, are used to construct a kinematic wave description for the settling and compaction of an initially fluidized bed of fine powder. Both flux laws are simple generalizations of the Richardson-Zaki equation. The continuous flux law is found to produce two regimes during settling and requires an infinite time for complete compaction. The discontinuous flux law produces up to three regimes during settling and requires a finite time for complete compaction. The discontinuous flux law predicts that the depth of the fully compacted bed increases with a constant speed either due to a contact discontinuity or a simple shock; that initially the head of the bed falls with constant speed due to a simple shock. The predictions of the continuous flux law are similar except that the bed does not fully compact anywhere. An elastic bulk modulus for the solid phase is introduced, resulting in a non-linear convective-diffusion equation, which describes approximately the voidage changes in the settling bed. It is conjectured that the initial settling of the bed is described by a hyperbolic equation, but finally, a diffusive equation may determine voidage evolution.