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We consider low-complexity, all-optical multi-stage networks with distributed arbitration achieved through minimal per-node buffering. To enhance the saturation throughput of such networks while maintaining low latency at low loads, we examine a novel combination of deterministic (prescheduled) and speculative (eager) packet injections. Prescheduled injections are performed in a time-division-multiplexing (TDM) manner, whereas eager injections follow a packet multiplexing paradigm. Prescheduled injections aim at reducing contention in the fabric, and sustain network throughput when the load is high. Eager injections, on the other hand, ignore the TDM schedule, thus allowing low latency communication when contention is low. In our set of rules that govern the interaction between prescheduled and eager packets, eager packets can be intentionally dropped when they block the progress of prescheduled ones. At the same time a highly efficient end-to-end reliable delivery scheme, implemented at the host adapters, deals with random packet losses in the optical domain, and also recovers the dropped eager packets. Computer simulations demonstrate that our approach can render low-complexity networks, which are amenable to an all-optical implementation, attractive for use in computer interconnects.