To support paediatric cardiologists in prognostic assessment and treatment planning, a decision-theoretic network for congenital heart disease is being constructed. The network is built in collaboration with a domain expert, using modelling methods commonly advocated in the literature. Although these methods prove to be useful in many cases, it was found that in some situations their applicability falls short. These situations and their associated problems are described. Techniques that have been developed to e ectively deal with the problems are presented.