We have investigated the effects of disorder-induced band tailing on deep levels in compound semiconducting alloys, such as GaAs and AlxGa1−xAs. In particular, we have eliminated the assumption of Gaussian broadening of the defect density of states proposed earlier by others on the basis of the central-limit theorem. The expressions derived for the transient capacitance in the presence of the disorder-induced band tailing are quite different from previously published results and indicate that the form of the broadening function is quite sensitive to, and should closely reflect, the underlying physical environment. We applied this theory to the investigation of the deep-level transient spectra (DLTS) and isothermal capacitance transient spectra (ICTS) in GaAs and AlxGa1−xAs. Our results indicate that standard experimental measurements with DLTS and ICTS, in general, can underestimate the activation energy, capture cross section, etc., even in the case of weak disorder.