TCP’s congestion control is deliberately cautious, avoiding network overloads by starting with a small initial window and then iteratively ramping up. As a result, it often takes flows several round-trip times to fully utilize the available bandwidth. In this paper we propose RC3, a technique to quickly take advantage of available capacity from the very first RTT. RC3 uses several levels of lower priority service and a modified TCP behavior to achieve near-optimal throughputs while preserving TCP-friendliness and fairness. We implement RC3 in the Linux kernel and in NS-3. In common wide-area scenarios, RC3 results in over 40% reduction in average flow completion times, with strongest improvements—more than 70% reduction in flow completion time—seen in medium to large sized (100KB-3MB) flows.