The scattering of electrons by phonons in semiconductors has been assumed to be dominated by the lowest-order process involving a single phonon. Using a new numerical approach to incorporate the next-leading-order process involving two phonons into high-field transport calculations from first principles, the authors find here that the two-phonon process contributes nearly as much as the single-phonon process to high-field transport phenomena. This finding resolves a long-standing discrepancy regarding the strength of intervalley scattering in GaAs as determined from different experimental methods.