We use simple scaling and symmetry arguments to deduce the following properties of spacetimes consisting of point test particles orbiting Kerr black holes. (a) The angular momentum at spatial and null infinity, and the angular momentum flux at null infinity, are well defined in the sense that the ambiguities in these quantities are smaller than the quantities themselves by one or more factors of the dimensionless mass ratio (mass of test particle)/(mass of black hole). (b) If the total angular momentum of the spacetime is taken to point in the z direction, then the x and y components of angular momentum flux vanish, and consequently the vectorial angular momentum flux does not yield enough information to infer the radiation-reaction driven evolution of the Carter constant in the adiabatic regime. (c) No linear momentum is radiated by the system in the adiabatic regime; the black hole only gets a kick by virtue of the breakdown of the adiabatic approximation during the final plunge. The first property also holds in arbitrary stationary spacetimes.