Bleaching effect, i. e., the absorption of a crystal to the visible lights is decreased after the crystal is illuminated by ultraviolet light, has been observed in congruent LiNbO3:Fe:Cu crystals. Based on this bleaching effect, two three-step recording schemes are proposed to record nonvolatile photorefractive holograms in LiNbO3:Fe:Cu, which use two red laser beams and an ultraviolet illumination selectively for the writing of charge grating in the shallow Fe centers, the developing of charge grating in the deep Cu centers by transferring the Fe grating, and the fixing of only the Cu grating for unerasable read-out. Experimental results show that the technique including recording phase by two interfering red beams and fixing phase by both UV light and a coherent red beam is optimal. The theoretical verification and optimal concentration are also simulated. As a conclusion, a comparison on the lithium niobate crystals of the same double doping system of Fe:Mn, Ce:Mn, Ce:Cu and Fe:Cu for nonvolatile holographic storage is outlined.