Void ordering has been observed in very different radiation environments ranging from metals to ionic crystals bombarded with energetic particles. The void ordering is often accompanied by a saturation of the void swelling with increasing irradiation dose, which makes an understanding of the underlying mechanisms to be both of scientific significance and of practical importance for nuclear engineering. We show that both phenomena can be explained by the original mechanism based on the anisotropic energy transfer provided by self-focusing discrete breathers or quodons (energetic, mobile, highly localized lattice solitons that propagate great distances along close-packed crystal directions). The interaction of quodons with voids can result in radiation-induced “annealing” of selected voids, which results in the void ordering under special irradiation conditions. We observe experimentally radiation-induced void annealing by lowering the irradiation temperature of nickel and copper samples pre-irradiated to produce voids or gas bubbles. The bulk recombination of Frenkel pairs increases with decreasing temperature resulting in suppression of the production of freely migrating vacancies (the driving force of the void growth). On the other hand, the rate of radiation-induced vacancy emission from voids due to the void interaction with quodons remains essentially unchanged, which results in void dissolution. The experimental data on the void shrinkage and void lattice formation obtained for different metals and irradiating particles are explained by the present model assuming the quodon propagation length to be in the micron range, which is consistent with independent data on the irradiation-induced diffusion of interstitial ions in austenitic stainless steel.