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We employ a combination of first-principles calculations and optical characterization experiments to explain the mechanism by which Ga doping prevents the trapping of free carriers due to shallow traps in REAlO garnet scintillators (where RE represents a rare-earth cation). Specifically, we confirm that Ga doping does not reduce the defect concentration (defect engineering), but rather leads to shifts in the valence and conduction bands such that the energy level of shallow defects is no longer in the forbidden gap where electrons can be trapped (band-gap engineering).