Collision-induced vibrational energy transfer has been studied from four levels [30(2) (E(vib) = 240 cm(-1)), 8(2) (E(vib) = 361 cm(-1)), 27(1) (E(vib) = 403 cm(-1)) and 6(1) (E(vib) = 410 cm(-1))] in S-1 p-difluorobenzene in supersonic free jet expansions of He, Ne, Ar, and Kr at similar to 30-40 K. In broad terms the trends are similar to those observed previously in studies of aromatics : the transfer is highly selective, and one quantum changes in the low frequency modes are preferred. However, a significant collision partner dependence is observed, whereby changing from He through to Kr causes a substantial increase in multiple quanta (Delta upsilon>1) transfer. SSH-T calculations fail to capture this trend, The preference for Delta upsilon>1 transfer appears to be enhanced as the interaction time and attractive force on the collision partner increase. Consequently, it is predicted that (i) differences in the state-to-state branching ratios between collision partners will increase as the temperature is lowered; (ii) for a particular collision partner there will be an increase in Delta upsilon>1 transfer with decreasing temperature; and (iii) Delta upsilon>1 transfers will be most important for collision partners with small velocities (i.e., large masses), large intermolecular potential well depths (epsilon) and size (sigma). The nearly isoenergetic 27(1) and 6(1) levels have virtually identical state-to-state branching ratios for Ar and small differences are observed for He. This suggests that the branching ratios are not particularly sensitive to the initial vibrational motion. Relaxation of 6(1) and 27(1) is inefficient compared with relaxation from 30(2) and 8(2).