In multi-core ASICs, processors and other compute engines need to communicate with memory blocks and other cores with latency as close as possible to the ideal of a direct buffered wire. However, current state of the art networks-on- chip (NoCs) suffer, at best, latency of one clock cycle per hop. We investigate the design of a NoC that offers close to the ideal latency in some preferred, run-time configurable paths. Processors and other compute engines may perform network reconfiguration to guarantee low latency over different sets of paths as needed. Flits in non-preferred paths are given lower priority than flits in preferred ones, and suffer a delay of one clock cycle per hop when there is no contention. To achieve our goal, we use the "madpostman" [5] technique: every incoming flit is eagerly (i.e. speculatively) forwarded to the input?s preferred output, if any. This is accomplished with the mere delay of a single pre-enabled tri-state driver. We later check if that decision was correct, and if not, we forward the flit to the proper output. Incorrectly forwarded flits are classified as dead and eliminated in later hops. We use a 2D mesh topology tailored for processor-memory communication, and a modified version of XY routing that remains deadlock-free. Our evaluation shows that, for the preferred paths, our approach offers typical latency around 500 ps versus 1500 ps for a full clock cycle or 135 ps for an ideal direct connect, in a 130 nm technology; non-preferred paths suffer a one clock cycle delay per hop, similar to that of other approaches. Performance gains are significant and can be proven greatly useful in other application domains as well.