We investigate the group key management problem for broadcasting applications. Previous work showed that, in handling key updates, batch rekeying can be more cost-effective than individual rekeying. One model for batch rekeying is to assume that every user has probability p of being replaced by a new user during a batch period with the total number of users unchanged. Under this model, it was recently shown that an optimal key tree can be constructed in linear time when p is a constant and in O(n ⁴) time when p →0. In this paper, we investigate more efficient algorithms for the case p →0, i.e., when membership changes are sparse. We design an O(n) heuristic algorithm for the sparse case and show that it produces a nearly 2-approximation to the optimal key tree. Simulation results show that its performance is even better in practice. We further design a refined heuristic algorithm and show that it achieves an approximation ratio of 1 + ε as p →0.