Percolating porosity as a specific type of deformation-induced was discovered in ultrafine-grained (UFG) Cu produced by equal channel angular pressing (Ribbe et al., Phys Rev Lett 2009;102:165501). The stability of this defect type against annealing under various conditions is investigated for UFG Cu of different purity levels. The porosity is found to withstand the annealing treatments up to 1073K for several hours in purified Ar atmosphere, despite significant microstructure transformation. Annealing at 1313K in Ar removes the percolating porosity, as do relatively short heat treatments at 427K in a hydrogen-containing atmosphere. Quasi-hydrostatic pressure applied at moderate temperatures, e.g. 1GPa at 423K, eliminates the percolating porosity, too. A model of porosity evolution, which accounts for the experimental findings, is suggested.