Bandwidth reservation has been increasingly used to provide QoS for various network applications. To accommodate a high-priority bandwidth reservation request (BRR), the bandwidth scheduler sometimes needs to preempt existing bandwidth reservations that have been made for BRRs with a lower priority, which is traditionally known as connection preemption. When such preemption is unavoidable, one primary goal of bandwidth scheduling is to minimize the disruption to existing reservations. In this paper, we study the problem of bandwidth reservation preemption for two types of BRRs, bandwidth- and data transfer- oriented, respectively, on one given link of the scheduling network with two different objectives: (i) minimize the number and then the total bandwidth of existing bandwidth reservations to be preempted, and (ii) minimize the total bandwidth and then the number of existing bandwidth reservations to be preempted. We prove these four problems to be NP-complete and propose a heuristic algorithm for each. We also design baseline heuristic algorithms for performance comparison. Extensive simulation results show that the proposed heuristic algorithms outperform those in comparison.