Minimizing latency and power are key goals in the design of NoC routers. Different proposals combine lookahead routing and router bypass to skip the arbitration and buffering stages of their pipeline, reducing router delay to a single-cycle. However, the conditions to use the bypass are unnecessarily conservative, requiring completely empty buffers in the intermediate routers. This restricts the amount of flits that use the bypass, increasing average latency and power.This paper introduces Non-Empty Buffer Bypass (NEBB), a mechanism that allows to bypass flits even if the buffers to bypass are not empty. The mechanism applies to wormhole and virtual-cut-through, each of them with different advantages. NEBB-Hybrid is proposed to employ the best flow control in each situation, maximizing the utilization of the bypass.The proposals have been evaluated using Booksim. Results show up to 75% reduction of the buffered flits for single-flit packets, which translates into latency and dynamic power reductions of up to 30% and 23% respectively. For bimodal traffic, these improvements are 20% and 21% respectively. Additionally, the bypass utilization is largely independent of the number of VCs when using shared buffers and very competitive with few private ones, allowing to simplify the allocation mechanisms.