Ray data sets describing light sources for illumination commonly contain starting points, directions and fl flux, and sometimes color. Simply adding luminance in addition to the flux which is already there, we gain useful design options not available otherwise. Adding luminance provides all information needed to apply the abstract, phase space based, concept of selecting maximum flux from given ètendue to real sources. Many light sources, e.g. arc lamps for projection, are used in rotationally symmetric optical systems. It is well known that the conservation of skewness imposes additional constraints on which parts of the source phase space can be transferred to the target. While it has been impractical in the past to apply this concept in practice, especially for sources with inhomogeneous luminance, we show how ray data sets including luminance can be readily used to determine fundamental upper limits on flux transfer efficiency in these cases, providing a valuable benchmark for actual optical designs.