Luminescent solar concentrators, potential solar energy devices for use in urban settings, suffer from considerable loss of light from their surfaces. The use of a selective reflector transparent to light that can be absorbed by the embedded fluorescent dye molecules but reflective towards dye-emitted light, could improve performance. One such reflector is the chiral nematic (cholesteric) liquid crystal. However, cholesteric liquid crystals often have two disadvantages: the reflection bandwidth is narrow, and even more importantly, there is considerable angular dependence in the reflection band, resulting in the loss of absorbed light at steep incidence angles. In this work we examine the possibility of using broadband cholesterics and 'special dispersion' cholesterics. These special dispersion cholesterics should have reduced angular dependence, and we present calculations demonstrating how using these selective reflectors on top of luminescent solar concentrators could significantly improve performance of the device under indirect lighting conditions consistent with what would be encountered in the built environment.Index Terms -broadband cholesteric liquid crystals, luminescent solar concentrator.