A firewall is a security guard placed at the point of entry between a private network and the outside Internet such that all incoming and outgoing packets have to pass through it. The function of a firewall is to examine every incoming or outgoing packet and decide whether to accept or discard it. This function is conventionally specified by a sequence of rules, where rules often conflict. To resolve conflicts, the decision for each packet is the decision of the first rule that the packet matches. The current practice of designing a firewall directly as a sequence of rules suffers from three types of major problems: (1) the consistency problem, which means that it is difficult to order the rules correctly; (2) the completeness problem, which means that it is difficult to ensure thorough consideration for all types of traffic; (3) the compactness problem, which means that it is difficult to keep the number of rules small (because some rules may be redundant and some rules may be combined into one rule). To achieve consistency, completeness, and compactness, we propose a new method called structured firewall design, which consists of two steps. First, one designs a firewall using a firewall decision diagram instead of a sequence of often conflicting rules. Second, a program converts the firewall decision diagram into a compact, yet functionally equivalent, sequence of rules. This method addresses the consistency problem because a firewall decision diagram is conflict-free. It addresses the completeness problem because the syntactic requirements of a firewall decision diagram force the designer to consider all types of traffic. It also addresses the compactness problem because in the second step we use two algorithms (namely FDD reduction and FDD marking) to combine rules together, and one algorithm (namely firewall compaction) to remove redundant rules. Moreover, the techniques and algorithms presented in this paper are extensible to other rule-based systems such as IPsec rules.