The electronic spectrum of alternant polycyclic aromatic hydrocarbons (PAHs) includes two singlet excited states that are often denoted (1)La and (1)Lb. Time-dependent density functional theory (TD-DFT) affords reasonable excitation energies for the (1)Lb state in such molecules, but often severely underestimates (1)La excitation energies and fails to reproduce observed trends in the (1)La excitation energy as a function of molecular size. Here, we examine the performance of long-range-corrected (LRC) density functionals for the (1)La and (1)Lb states of various PAHs. With an appropriate choice for the Coulomb attenuation parameter, we find that LRC functionals avoid the severe underestimation of the (1)La excitation energies that afflicts other TD-DFT approaches, while errors in the (1)Lb excitation energies are less sensitive to this parameter. This suggests that the (1)La states of certain PAHs exhibit some sort of charge-separated character, consistent with the description of this state within valence-bond theory, but such character proves difficult to identify a priori. We conclude that TD-DFT calculations in medium-size, conjugated organic molecules may involve significant but hard-to-detect errors. Comparison of LRC and non-LRC results is recommended as a qualitative diagnostic.