Femtosecond transmission spectra of highly polar CdTe are compared to more covalent GaAs contrasting semiclassical kinetics with two-time quantum kinetics based on the Dyson equation. Nonequilibrium heavy holes in CdTe show ultrafast energy redistribution via the Fröhlich mechanism even if photoexcited below the LO phonon energy. This subthreshold relaxation is a genuine quantum kinetic effect. It gains importance if the polaron self-energy is comparable to the phonon energy. Conservation of the free-particle energies is not required under these conditions.