Luminescent solar concentrators would allow for high concentration if losses by reabsorption and escape could be minimized. We introduce a phosphor with close-to-optimal luminescent properties and hardly any reabsorption. A problem for use in a luminescent concentrator is the large scattering of this material; we discuss possible solutions for this. Furthermore, the use of broad-band cholesteric filters to prevent escape of luminescent radiation from this phosphor is investigated both experimentally and using simulations. Simulations are also used to predict the ultimate performance of luminescent concentrators.