As-grown single-crystal InP nanowires, covered with a surface oxide, show a photoluminescence efficiency that strongly varies from wire to wire. We show that the luminescence efficiency of single-crystal InP nanowires can be improved by photoassisted wet chemical etching in a butanol solution containing HF and the indium-coordinating ligand trioctylphosphine oxide. Electron-hole photogeneration, electron scavenging, and oxidative dissolution combined with surface passivation by the indium-coordinating ligand are essential elements to improve the luminescence efficiency. Time traces of the luminescence of surface-passivated wires show strong oscillations resembling the on-off blinking observed with single quantum dots. These results reflect the strong influence of a single or a few nonradiative recombination center(s) on the luminescence properties of an entire wire.