We study link scheduling in networks with small router buffers, with the goal of minimizing the guaranteed packet loss rate bound for each ingress-egress traffic aggregate (connection). Given a link scheduling algorithm (a service discipline and a packet drop policy), the guaranteed loss rate for a connection is the loss rate under worst-case routing and bandwidth allocations for competing traffic. Under simplifying assumptions, we show that a local min-max fairness property with respect to apportioning loss events among the connections sharing each link, and a condition on the correlation of scheduling decisions at different links are two necessary and (together) sufficient conditions for optimality in the minimization problem. Based on these conditions, we introduce a randomized link-scheduling algorithm called Rolling Priority where packet scheduling at each link relies exclusively on local information. We show that RP satisfies both conditions and is therefore optimal.