The mechanism of collisional energy transfer in collisions between a highly excited polyatomic and a monatomic bath gas is investigated for benzene–rare-gas systems by carrying out both vibrational close-coupling, infinite-order sudden quantum-scattering computations and classical trajectory calculations with a high degree of initial internal excitation; the quantum calculations involved up to two vibrational modes. It is found in the quantum-scattering calculations that if one of the vibrational modes is of low frequency (and particularly if it is an out-of-plane motion), then the cross-section for transferring large amounts of energy is particularly large, and involves multi-quantum transitions. Although the quantum simulations have far fewer modes (and hence involve a far lower density of states) than in an actual system, this suggests that low-frequency/out-of-plane modes are prominent in transferring significant amounts of energy (and perhaps in ‘supercollisions’), since a microcanonical ensemble in an actual system at high internal energy will contain a large proportion of states with high excitation in low-frequency modes. Both the quantum and trajectory results are consistent with a supercollision mechanism which is a head-on collision between a bath-gas atom and a rapidly moving substrate atom involved in a large-amplitude motion such as occurs with a highly excited low-frequency out-of-plane vibration.