Single layers of MoS 2 and MoSe 2 were optically pumped with circularly polarized light and an appreciable polarization was initialized as the pump energy was varied. The circular polarization of the emitted photoluminescence was monitored as a function of the difference between the excitation energy and the A-exciton emission at the K-point of the Brillouin zone. Our results show a threshold of twice the LA phonon energy, specific to the material, above which phonon-assisted intervalley scattering causes depolarization. In both materials this leads to almost complete depolarization within ~100 meV above the threshold energy. We identify the extra kinetic energy of the exciton (independent of whether it is neutral or charged) as the key parameter for presenting a unifying picture of the depolarization process.