In transport-layer protocols such as TCP over ATM networks, a packet is discarded when one or more cells are lost in that packet, and the destination node then requires its source to retransmit the corrupted packet. Therefore, once one of the cells constituting a packet is lost, the subsequent cells of the corrupted packet waste network resources. Thus, discarding those cells will enable us to efficiently utilize the network resources and improve the packet loss probability. We focus on tail dropping (TD) and early packet discard (EPD) as selective cell discard schemes which force the switches to discard some of the arriving cells instead of relaying them. We exactly analyze the packet loss probability in a system applying these schemes. Their advantage and limits are then discussed based on numerical results derived through the analysis.