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Low Earth orbit (LEO) satellite networks are deployed as an enhancement to terrestrial wireless networks in order to provide broadband services to users regardless of their location. In addition to ensuring global coverage, LEO satellite systems support communications with hand-held devices and offer low-cost access, making them promising platforms for military communications and for personal communication services (PCS). The main contribution of this work is to propose RADAR - refined admission detecting absence region - a novel call admission control and handoff management scheme for multimedia LEO satellite networks. A key ingredient in our scheme is a companion predictive bandwidth allocation strategy that exploits the topology of the network and contributes to maintaining high bandwidth utilization. The performance of RADAR is compared to that of three recent schemes proposed in the literature. Simulation results show that our scheme offers a very low call dropping probability, providing for reliable handoff of on-going calls, as well as a low call blocking probability for new call requests, while still ensuring high bandwidth utilization.