We measure for the first time transient absorption spectra of individual CdSe nanowires with about 10 nm diameter. Confinement of the carrier wave functions leads to discrete states which can be described by a six-band effective mass model. Combining transient absorption and luminescence spectroscopy allows us to track the excitation dynamics in the visible and near-infrared spectral range. About 10% of all absorbed photons lead to an excitation of the lowest energy state. Of these excitations, less than 1% lead to a photon in the optical far-field. Almost all emission is reabsorbed by other parts of the nanowire. These findings might explain the low overall quantum efficiency of CdSe nanowires.