Frameworks for analyzing the risks of emerging diseases and invasive species often have relied on unstructured estimates of likelihoods and consequences. We suggest a flexible alternative that offers more transparent analysis without need for additional data. Its strength lies in explicit and complementary treatment of technical and social judgments. We describe a system in which cognitive maps, Bayes nets, and multicriteria analysis can be used in tandem to structure a problem, identify exposure pathways, combine data and expert judgement to estimate the likelihoods, and assess consequences of alternative decisions. These tools may be employed in participatory settings or as part of standard regulatory practice. We illustrate this approach with an assessment of the management of an emerging disease that poses a hazard to Australia.