- The optical performance of axisymmetric radiation concentrators and illuminators that are derived when two-dimensional edge-ray designs are rotated about their optic axis is investigated. Of particular interest are devices with spherical and cylindrical absorbers or light sources, for which the inherent ray rejection can be substantial. From the principle of etendue (phase-space) conservation, a lower bound for ray rejection can be established. With computer ray tracing, we demonstrate that this bound underestimates the actual ray rejection by only a few percent at most. Hence, to a good approximation, it can be used as an equality in analytic predictions of characteristic efficiency-concentration curves. By designing for absorbers or sources with a bald spot, the full range of efficiency and flux concentration values can be realized and the trade-off between them can be quantified. The optical performance of these edge-ray designs is also compared against fundamental upper bounds on the flux concentration and efficiency of axisymmetric devices.