The basic idea that the instantaneous normal modes of a fluid govern its short-time dynamics has recently been used to arrive at theories for solvation dynamics and for vibrational population relaxation, theories not quite as distinct as one might have guessed for such different-looking relaxation processes.-Both theories, in particular, revolve around the weighted spectra of instantaneous normal modes we call the influence spectra, with the distinctions between the different problems showing up largely in the different weightings. We show in this paper that the influence spectra reveal a surprising amount of commonality in these two processes. For the models we consider, involving an atomic solvent and relatively short-ranged intermolecular forces, the two kinds of averaged influence spectra have virtually identical shapes. Moreover, examining a single configuration of the fluid at a time reveals that both spectra are strongly inhomogeneously broadened - that is, relatively few modes contribute at any instant, despite the breadth of the configurationally averaged spectra. What is apparently responsible for this common behavior is yet a deeper similarity. If one focuses specifically on the contributing modes, it becomes clear that the reason they contribute is their ability to move one or two solvent atoms in the immediate vicinity of the solute. This observation implies that it should always be possible for us to construct a set of effective modes involving motions that would be no more elaborate than few-body vibrations but that would still allow us to predict the influence spectra. We demonstrate just such predictions in this paper, using the one or two simple binary modes which vibrate the solute against its nearest-neighbor solvent atom. Binary modes as a class account for no more than the highest 10% of the instantaneous-normal-mode frequencies, yet we find that the solute-solvent binary modes are not only responsible for all of the high frequency aspects of solvation dynamics and vibrational population relaxation, they account in a quantitative sense for the majority of both influence spectra. At least in these examples, the bulk of the mechanism by which short-time relaxation takes place is evidently no more complicated than pair motions - what the rest of the solvent decides is how and when these motions take place.