We show that a number of PD-LGD correlation models that have been proposed in the literature, are special cases of a more general framework.  We explore this framework in detail and make several interesting observations. For instance, (i) we identify a common modelling error that tends to overestimate economic capital, and (ii) we find that the relationship between account-level correlations (modelling inputs) and portfolio-level correlations (modelling outputs) is surprisingly weak.