Designing security measures often involves trade-offs between various types of objectives. Multiple stakeholders may have conflicting demands and may have different ideas on how to resolve the resulting design conflicts. This paper reports on an application of value-sensitive design. Based on argumentation theory and social values, the paper develops a structured approach for discussing design conflicts, called value-based argumentation. The application domain examined in the paper is concerned with physical safety and security issues that arise in cross-border shipments. We first (...) identify the kinds of dialogues that take place in this domain, in particular, audit dialogues to determine whether security measures comply with regulations. Based on argumentation theory we develop a formal language and a diagramming approach intended to facilitate parties in identifying, discussing and reaching agreement about security risks and corresponding mitigation measures. Trade-offs can be dealt with by making underlying values explicit. Using a stylized example, the approach was successfully taught to practitioners working with EU customs regulations. Practitioners generally found the approach helpful, in particular to bring out implicit underlying motivations. We conclude by discussing how our approach can be generalized to other kinds of dialogues involving design conflicts. (shrink)