Inter-Landau-level relaxation in two-dimensional electron and hole gases in high magnetic fields is strongly affected by the extent, lambda(z), of the electronic wavefunction perpendicular to the two-dimensional channel. As the field is increased, the suppression of the one-acoustic-phonon (cyclotron phonon) emission process that occurs when the phonon wavenumber at the cyclotron frequency exceeds lambda(z)-1 causes two-acoustic-phonon emission to replace one-phonon emission as the dominant relaxation process. The field at which this occurs has been calculated. The net reduction in relaxation rate is believed to be partly responsible for the sensitivity of the optical detection of cyclotron resonance in two-dimensional electron gas systems. In zero magnetic field, the two-phonon process should also contribute significantly to the energy and momentum relaxation of hot electrons.