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The well-known problem of reliability of partial photoneutron cross-section data obtained using beams of quasimonoenergetic annihilation photons was discussed. Noticeable disagreements between data from various experiments were analyzed using physical data reliability criteria. The experimentally–theoretical method for evaluation of reaction cross sections satisfied physical criteria was used and new reliable data were obtained for many nuclei. The disagreements between newly evaluated cross sections and data from the IAEA Digital Photonuclear Data Library were discussed.