Collision-induced vibrational energy transfer has been studied from four levels [302 (Evib=240 cm-1), 82 (Evib=361 cm-1), 271 (Evib=403 cm-1) and 61 (Evib=410 cm-1)] in S1 p-difluorobenzene in supersonic free jet expansions of He, Ne, Ar, and Kr at ∼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 (|Δv]>1) transfer. SSH-T calculations fail to capture this trend. The preference for |Δv|>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 |Δv|>1 transfer with decreasing temperature; and (iii) |Δv|>1 transfers will be most important for collision partners with small velocities (i.e., large masses), large intermolecular potential well depths (∈) and size (σ). The nearly isoenergetic 271 and 61 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 61 and 271 is inefficient compared with relaxation from 302 and 82.