The motion of a radiating point particle in the Kerr spacetime can be represented by a series of geodesics whose constants of motion change slowly over its motion. In the case of energy and axial angular momentum, there are conserved currents, defined for the field, whose fluxes at infinity and the horizon directly determine the evolution of these constants of motion. This relationship between the properties of point-particle motion and fluxes of conserved currents is known as a "flux-balance law". Despite the flux-balance laws for energy and axial angular momentum, the third constant of motion in Kerr, the Carter constant, has no known flux-balance law. While there are conserved currents that can be defined for the field that are, in certain senses, "associated with the Carter constant", the fluxes of these currents are not clearly related to the Carter constant for the particle. In this talk, we present our recent efforts to find such flux-balance laws, in the case of a point particle in Kerr that is coupled to a scalar field.