Packet-switched interconnect fabric is a promising on-chip communication solution for many-core architectures. It offers high throughput and excellent scalability for on-chip data and protocol transactions. The main problem posed by this communication fabric is the potentially-high and nondeterministic network latency caused by router data buffering and resource arbitration. This paper describes a new method to minimize on-chip network latency, which is motivated by the observation that only a small percentage of on-chip data and protocol traffic is latency-critical. Existing work focusing on minimizing average network latency is thus suboptimal.