It is now well confirmed that the influence of temperature on the fall-off behavior of dissociation recombination and chemically-activated reactions can be dramatic. For single-well, single-product dissociation reactions, it is customary to approximate these fall-off surfaces using extensions of Lindemann’s empirical expression. We consider here chemical-activation and dissociation reactions possessing multiple wells and multiple products. We show that direct approximation of the rate coefficients via Chebyshev expansions yields reliable and accurate representations of their pressure and temperature dependences, which are superior to those from a Lindemann approach to fit the form factor representing the fall-off surface. The superiority of the method is demonstrated in a study of seven channels corresponding to four different reactions important in combustion chemistry over the ranges 300-3,000 K and 0.02-200 atm.