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The role of recombination during a common-envelope event has been long debated. Many studies have argued that much of hydrogen recombination energy, which is radiated in relatively cool and optically-thin layers, might not thermalise in the envelope. On the other hand, helium recombination contains 30% of the total recombination energy, and occurs much deeper in the stellar envelope. We investigate the distinct roles played by hydrogen and helium recombination in a common-envelope interaction experienced by a 12 solar mass red supergiant donor. We perform adiabatic, 3D hydrodynamical simulations that (i) include hydrogen, helium, and molecular hydrogen recombination, (ii) include hydrogen and helium recombination, (iii) include only helium recombination, and (iv) do not include recombination energy. By comparing these simulations, we find that the addition of helium recombination energy alone ejects 30% more envelope mass, and leads to a 16% larger post-plunge-in separation. Under the adiabatic assumption, adding hydrogen recombination energy increases the amount of ejected mass by a further 40%, possibly unbinding the entire envelope, but does not affect the post-plunge separation. Most of the ejecta becomes unbound at relatively high (>70%) degrees of hydrogen ionisation, where the hydrogen recombination energy is likely to expand the envelope instead of being radiated away.