The influence of the energy dependence of [Delta E](down) on the shape of falloff curves in unimolecular reactions is investigated using two model systems : the decomposition of C2H5 and the isomerization of cycloheptatriene (CHT). An exponential-down model of collisional energy transfer is used with [Delta E](down)(E) proportional to E(i), where i = 1 for the C2H5 decomposition and i = 1/2 for the CHT isomerization. It is demonstrated that neglect of the energy dependence of [Delta E](down) in the fitting of experimental falloff data may yield significant discrepancies between low-pressure and high-pressure results.