Stochastic scenario trees are a new and popular method by which surveillance systems can be analyzed to demonstrate freedom from pests and disease. For multiple component systems-such as a combination of a serological survey and systematically collected observations-it can be difficult to represent the complete system in a tree because many branches are required to represent complex conditional relationships. Here we show that many of the branches of some scenario trees have identical outcomes and are therefore redundant. We demonstrate how to prune branches and derive compact representations of scenario trees using matrix algebra and Bayesian belief networks. The Bayesian network representation is particularly useful for calculation and exposition. It therefore provides a firm basis for arguing disease freedom in international forums.