Copyright protection is a major issue in online content-distribution services and many key-management schemes have been proposed for protecting content. Key-distribution processes impose large burdens even though the communications bandwidth itself is restricted in the distribution of mobile content provided to millions of users. Mobile devices also have low computational capacities. Thus, a new scheme of key management, where the load on the key-distribution server is optimal and loads on clients are practical, is required for services. Tree-based schemes aim at reducing the load on the server and do not take reducing the load on clients into account. The load on clients is minimized in a star-based scheme, on the other hand, while the load on the server increases in proportion to the number of clients. These structures are far from being scalable. We first discuss a relaxation of conventional security requirements for key-management schemes in this paper and define new requirements to improve the efficiency of the schemes. We next propose the τ-gradual key-management scheme. Our scheme satisfies the new security requirements and loads on the server, and it has far fewer clients than conventional schemes. It uses an intermediate configuration between that of a star- and a tree-structure that allows us to continuously change it by controlling the number of clients in a group, m_max. The scheme can be classified as τ-star-based, τ-tree-based, or τ-intermediate depending on the parameter, m_max. We then present a quantitative evaluation of the load on the server and clients using all our schemes based on practical assumptions. The load on the server and that on clients involves a trade-off with the τ-intermediate scheme. We can construct an optimal key-management structure according to system requirements using our schemes, while maintaining security. We describe a concrete strategy for setting parameter m_max. Finally, we present general parameter settings by which loads on both the server and clients using the τ-intermediate scheme are lower than those using the τ-tree-based scheme.