Abstract: A TN3270 server (26) that forwards a 3270 data stream from a Systems Network Architecture ("SNA") connection (28) to a Transmission Control Protocol ("TCP") connection (24) monitors the TCP connection for segments that acknowledge thereby-transmitted bytes. It also keeps track of the unacknowledged-byte window sizes specified by received TCP-connection segments. It responds with a pacing response to a pacing-request-containing SNA message only when forwarding of previously received information from the SNA can be completed without resulting in a number of unacknowledged bytes that exceeds the specified window size.