BitTorrent has recently introduced LEDBAT, a novel application-layer congestion control protocol for data exchange. The protocol design assumes that network bottlenecks are at the access of the network, and that thus user traffic competes creating self-induced congestion. To relieve this phenomenon, LEDBAT is designed to quickly infer when self-induced congestion is approaching (by detecting relative changes of the one-way delay in the transmission path), and to react promptly by reducing the sending rate prior to the congestion occurrence. Previous work has however shown LEDBAT to be affected by a latecomer advantage, where newly arriving connections can starve already existing flows. In this work, we propose modifications to the congestion window update mechanism of LEDBAT that solve this issue, thus guaranteeing intra-protocol fairness and efficiency. Closed-form expressions for the stationary throughput and queue occupancy are provided via a fluid model, whose accuracy is confirmed by means of ns2 packet level simulations. Our results show that the proposed change can effectively solve the latecomer issue, furthermore without affecting the other original LEDBAT goals.