Generalized Template Theory (GTT: McCarthy and Prince 1994b, Urbanczyk 1995, 1996, 2000, 2006 and, from a different perspective, Downing 2006) is a theory developed within the overall framework of BRCT in which reduplicative size and shape are determined by classifying individual RED morphemes as roots vs.
A result of adopting the Dual Theory of reduplication is that the abstract morpheme RED that drives reduplication and reduplicative correspondence in BRCT plays no role either in phonological duplication or in morphological doubling.
Another advantage of recognizing the more limited role that correspondence plays in reduplication lies in the elimination of certain pathological predictions that BRCT has been observed to make for morphological reduplication.
This is the kind of phenomenon that BRCT handles well, except that BRCT overgenerates by predicting it in the areas of total and partial morphological reduplication, where it does not occur to the same degree as in the phenomena classified here as phonological duplication.
In sum, the prediction of BRCT that overapplication can be driven by correspondence is correct--but only for a restricted subset of types of reduplication, namely those driven by the phonology.