This article reports a generalized and systematic approach to the thermoluminescence (TL) dating of samples which suffer from anomalous fading. We hypothesize that the TL signal from each mineral phase is composed of a stable and an unstable portion. The decay of the unstable TL is accelerated thermally, until only stable TL remains. The dating is then carried out on this stable signal. The results, on four known-age, coeval samples, exhibiting gross anomalous fading (25-50% loss over a few days), indicate that many, if not all, samples may successfully be dated with this approach. -- AATA