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Many previous studies have shown that traditional TCP slow-start algorithm suffers performance degradation in high-speed and long-delay networks. This paper presents a sender-side enhancement, which makes use of TCP Vegas congestion-detecting scheme to monitor the router queue, and accordingly refines slow-start window evolution by introducing a two-phase approach to probe bandwidth more efficiently. Moreover, it achieves good fairness of bandwidth utilization in coexistence of multiple connections. Simulation results show that, compared with traditional slow-start and many other enhancements, it is able to significantly improve the startup performance without adversely affecting coexisting TCP connections.