For many applications, e.g. the daily tracking of market prices in front office systems, it is sufficient to consider a simplified CDO pricing model. In Volume I of this series such a simplified model was presented based on the assumption of a very large, homogeneous portfolio. However, e.g. for more detailed scenario analyses and the computation of hedge ratios, one has to relax these simplifying assumptions. In the current paper, several extensions of the CDO pricing model based on a Gumbel copula are discussed and possible implementations are presented. These extensions can be used to price CDO contracts on non-homogeneous pools.