Current congestion control approaches that attempt to provide fair bandwidth allocation among competing flows primarily consider only data rate when making decisions on which packets to drop. However, responsive flows with high round trip times (RTTs) can still receive significantly less bandwidth than responsive flows with low round trip times. This paper proposes a congestion control scheme called WHITE that addresses router unfairness in handling flows with significantly different RTTs. Using a best-case estimate of a flow's RTT provided in each packet by the flow source or by an edge router, WHITE computes a stabilized average RTT. The average RTT is then compared with the RTT of each incoming packet, dynamically adjusting the drop probability so as to protect the bandwidth of flows with high RTTs while curtailing the bandwidth of flows with low RTTs. We present simulation results and analysis that demonstrate that WHITE provides better fairness than other rate-based congestion control strategies over a wide-range of traffic conditions. The improved fairness of WHITE comes close to the fairness of Fair Queuing without requiring per flow state information at the router.