We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three-body recombination rate K3 where three free atoms interact to produce an atom-dimer pair, and the relaxation rate K rel where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for K3, namely the NTR (Near Threshold Resonance) regime behavior E −2 for negative scattering lengths and the NTS (Near Threshold Suppression) regime behavior E 2 for positive scattering lengths. We also confirm a previously found oscillatory behavior of K3 at higher energy E. Finally, we find that K rel behaves as E −1 in the NTR regime.