A facility for proxying network traffic between a pair of nodes is described. The facility receives packets traveling between the pair of nodes that together constitute a distinguished network connection. For each packet of the connection that is part of a transport protocol setup process, the facility updates a representation of the status of the setup process to reflect the packet, and forwards the packet to its destination without proxying the packet. For each packet of the connection that is subsequent to the setup process, the facility proxies the contents of the packet to the packet's destination.