We investigate the performance of TCP connections over ATM networks without ATM-level congestion control, and compare it to the performance of TCP over packet-based networks. For simulations of congested networks, the effective throughput of TCP over ATM can be quite low when cells are dropped at the congested ATM switch. The low throughput is due to wasted bandwidthas the congested link transmits cells from `corrupted' packets, i.e., packets in which at least one cell is dropped by the switch. We investigate two packet discard strategies which alleviate the effects of fragmentation. Partial Packet Discard, in which remaining cells are discarded after one cell has been dropped from a packet, improves throughput somewhat. We introduce Early Packet Discard, a strategy that prevents fragmentation and brings throughput up to maximal levels by having the switch drop whole packets prior to buffer overflow.