InN films grown by molecular beam epitaxy have been subjected to 2 MeV He{sup +} irradiation followed by thermal annealing. Theoretical analysis of the electron mobilities shows that thermal annealing removes triply charged donor defects, creating films with electron mobilities approaching those predicted for uncompensated, singly charged donors. Optimum thermal annealing of irradiated InN can be used to produce samples with electron mobilities higher than those of as grown films.