We consider the problem of packet scheduling in a network with small router buffers. The objective is to provide a statistical bound on the worst-case packet loss rate for a traffic aggregate (connection) routed along any network path, given a maximum permissible link utilization (load). This problem is argued to be of interest in networks providing statistical loss-rate guarantees to ingress-egress connections with fixed bandwidth demands. We introduce a scheduling algorithm for networks using perpacket transmission reservation. Reservations allow loss guarantees at the aggregate level to hold for individual flows within the aggregate. The algorithm employs randomization and traffic regulation at the ingress, and batch local scheduling at the links. It ensures that a large fraction of packets from each connection are consistently subject to small loss probability at every link. These packets are therefore likely to survive long paths. To obtain the desired loss-rate bound, we analyze the performance of the algorithm under global routing and bandwidth allocation scenarios that maximize the loss rate of a connection routed along an arbitrary network path. We compare the bound to that obtained using the scheduling algorithm that combines the FCFS service discipline and the drop-tail policy. We find that the proposed algorithm significantly improves the constraints on link utilization and path length necessary to achieve strong loss-rate guarantees.