A cell-discard method has been developed for use in networks supporting TCP-over-ATM traffic with an unspecified bit rate. In this "concentrated cell discard" (CCD) method, when an ATM switch becomes congested, consecutive cells are discarded from the front of the buffer, and cell discarding is suspended for a specified period of time. This method prevents TCP timeouts, which are the main reason for the decreasing TCP throughput in today's TCP-over-ATM networks, and shortens the duration of the congestion by avoiding the long delay experienced with the TCP fast-retransmission algorithm before the sender's TCP receives duplicate acknowledgments. Even though CCD does not consider TCP packet size or boundaries, the throughput with CCD was found by computer simulation to actually be higher than with early packet discard.