Non-exponential relaxation in disordered systems may be interpreted in terms of a distribution of exponential rate constants that arises naturally from a narrow, random distribution in the value of a structural parameter (distance or angle) which characterizes the inequivalent sites within the system. This analysis is applied to the decay of methyl radicals in glassy methanol and to other systems. In the former case, the underlying assumptions have been tested experimentally. Such an approach indicates in general terms which kind of disorder is responsible for the observed decay. It also offers the prospect of obtaining a detailed description of the microscopic structure of a reactive site.