Remote backup and some grid applications transfer large amounts of data over long distance networks. The throughput of TCP Reno and NewReno over LFNs (large fat pipe networks) is much smaller than application requirements. High speed protocols are being developed to overcome this problem. However, the fairness of these high speed protocols with conventional TCP (Reno or NewReno) is not sufficient in LFN. Some TCP based high speed protocols (e.g., TCP Westwood and BIC TCP) estimate available bandwidth to improve fairness. These protocols estimate available bandwidth on the sender side by using Ack packets, while UDT (UDP based data transfer protocol) is a high speed protocol that estimates available bandwidth on the receiver side by using packet pair algorithms. Estimating available bandwidth on the receiver side should be more accurate than estimating it with Acks. However, the fairness of UDT with conventional TCP and UDT itself over an LFN is not good enough. The UDT protocol estimates a much greater value than the actual available bandwidth when a network is congested. The UDT detects congestion too late in LFN environments. We propose gUDT (gentle UDT) and ERED to improve fairness over that currently provided in LFNs.