Recently, many group key management approaches based on the use of logical key trees have been proposed to address the issue of scalable group rekeying that is needed to support secure communications for large and dynamic groups. In this paper, we present two optimizations for logical key tree organizations that utilize information about the characteristics of group members to further reduce the overhead of group rekeying. First, we propose a partitioned key tree organization that exploits the temporal patterns of group member joins and departures to reduce the overhead of rekeying. Using an analytic model, we show that our optimization can achieve up to 31.4% reduction in key server bandwidth overhead over the unoptimized scheme. Second, we propose an approach under which the key tree is organized based on the loss probabilities of group members. Our analysis shows this optimization can reduce the rekeying overhead by up to 12.1%.