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Compared with direct-gap semiconductors, the valley degeneracy of silicon and germanium opens up new channels for spin relaxation that counteract the spin degeneracy of the inversion-symmetric system. Here the symmetries of the electron-phonon interaction for silicon and germanium are identified and the resulting spin lifetimes are calculated. Room-temperature spin lifetimes of electrons in silicon are found to be comparable to those in gallium arsenide, however, the spin lifetimes in silicon or germanium can be tuned by reducing the valley degeneracy through strain or quantum confinement. The tunable range is limited to slightly over an order of magnitude by intravalley processes., Comment: 7 pages, 3 figures, 13 tables