We propose a new broadcast encryption scheme based on the idea of ‘one key per each punctured interval’. Let r be the number of revoked users. In our scheme with p-punctured c-intervals, the transmission overhead is roughly \fracrp+1\frac{r}{p+1} as r grows. Our scheme is very flexible with two parameters p and c. We may take p as large as possible if a user device allows a large key storage, and set c as small as possible if the storage size and the computing power is limited. As variants of the proposed scheme, we further study a combination of a one-way chain and a hierarchical ring. This combination provides a fine-grained trade-off between user storage and transmission overhead. As one specific instance, the combination includes the subset difference (SD) scheme which is considered the most efficient one in the literature.