Luminescent solar concentrators (LSCs) have been studied for decades as an alternative to conventional lens-based optical concentrators for improving the performance and lowering the cost of high-efficiency photovoltaic solar converters. However, the Stokes shift from luminophores that comprise the LSC entails that the strategy cannot achieve the well-known Shockley–Queisser conversion efficiency limit of 33.7%, even theoretically. We show how aligned semiconductor nanorods with anisotropic dipolar photoluminescence can partially overcome losses due to the Stokes shift. We also outline LSC designs with conversion efficiency >33.7  %   and highlight how nanorods relax the demands on solar trackers in these proposals. Our analysis predicts efficiency increases even when nonradiative loss is comparable to current GaAs cells and when our models incorporate the experimentally measured anisotropy of colloidal dot-in-rod CdSe/CdS nanoparticles that we synthesized for this study. Fundamentally, these improvements result from the angular redistribution of light energy provided by the anisotropic, Stokes-shifted nanorod luminescence.