Several research and production networks now provide multiple Gbps dedicated connections to meet the demands of large data transfers over wide-area networks. Application throughputs, however, were not able to match these rates because the traditional transport methods have not been optimized for such connections. We propose a transport method based on stochastic approximation methods that: (a) stabilizes the source rate for peak utilization of connection bandwidth, and (b) adapts the acknowledgment interval to maximize the goodput at the receiver. We show the asymptotic stability and convergence of this method in maximizing the throughput over dedicated connections under fairly general conditions. Extensive experimental results indicate the effectiveness of this transport method in achieving file transfer throughputs that closely match iperf bandwidth measurements on dedicated connections of several thousand miles over UltraScience Net and ESnet, and also illustrate its superior performance on a local dedicated connection in comparison with existing methods.