We perform for the first time photoluminescence excitation (PLE) studies of individual nanocrystals (NCs) that reveal the structure of excited-state transitions not obscured by ensemble averaging. Single-NC PLE spectra strongly deviate from a traditional idealized picture of sharp, quasiatomic resonances. We detect only a few relatively narrow transitions (3-4 meV) at the band edge, while at higher spectral energies, we observe a broad structureless feature separated from the band-edge peaks by a >50 meV "minigap." These observations can be rationalized by analyzing hole intraband relaxation behavior.