Colloidal semiconductor nanorods have demonstrated potential as bright, stable, and polarized light sources. Emission of light in these and other nanocrystals proceeds through recombination of confined electron-hole pairs or excitons with tunable size-dependent resonant frequencies. Usually, their brightness is reduced by the "dark exciton"─a nonemissive state into which electron-hole pairs relax before recombining radiatively. Here we analyze the fine structure of exciton states in wurtzite CdSe nanorods and demonstrate that, for cylindrical nanorods of radii less than a critical value of