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TCP congestion-control is fairly inefficient in achieving high throughput in high-speed and dynamic-bandwidth environments. The main culprit is the slow bandwidth-search process used by TCP, which may take up to several thousands of round-trip times (RTTs) in searching for and acquiring the end-to-end spare bandwidth. Even the recently-proposed "highspeed" transport protocols may take hundreds of RTTs for this. In this paper, we design a new approach for congestion-control that allows TCP connections to boldly search for, and adapt to, the available bandwidth within a single RTT. Our approach relies on carefully orchestrated packet sending times and estimates the available bandwidth based on the delays experienced by these. We instantiate our new protocol, referred to as RAPID, using mechanisms that promote efficiency, queue-friendliness, and fairness. Our experimental evaluations on gigabit networks indicate that RAPID: (i) converges to an updated value of bandwidth within 1-4 RTTs; (ii) helps maintain fairly small queues; (iii) has negligible impact on regular TCP traffic; and (iv) exhibits excellent intra-protocol fairness among co-existing RAPID transfers. The rate-based design allows RAPID to be truly RTT-fair.