Persistent holograms are recorded locally with red light in a LiNbO>(3) crystal doped with Mg and Fe. Selective erasure is realized by use of a focused UV sensitizing light. We demonstrate the recording of 50 localized images as well as selective erasure in a 4 mm x 4 mm x 4 mm crystal. A comparison of the total recording time for M holograms obtained with the conventional distributed-volume recording and the localized methods is presented.