The disclosed embodiments provide a system that processes network packets. Upon receiving a first Transmission Control Protocol (TCP) header for a first TCP segment from a network link, the system immediately provides a portion of the first TCP header to a transport layer prior to receiving all payload data for the first TCP segment. Next, the system uses the transport layer to transmit a first acknowledgment of the first TCP segment to the network link, wherein the first acknowledgment reduces a round-trip time (RTT) associated with the first TCP segment.