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When a TCP sender receives three successive duplicate ACKs indicating a packet loss, loss differentiation algorithms (LDAs) distinguish wireless losses from congestion losses to improve TCP's performance in wireless networks. Although previous LDAs improved the accuracy of wireless loss discrimination, each LDA has a trade-off relationship between the accuracy of wireless loss discrimination and the accuracy of congestion loss discrimination based on its own threshold. To suggest good guidelines for deciding the best threshold to improve TCP's performance to the max, we observe the relationship between LDA's accuracy and TCP's performance improvement throughout the extensive simulations. Contrary to our expectations, the simulation results show that LDA's detection information itself is not sufficient to improve TCP's performance due to frequent spurious retransmission timeouts (RTO). The results emphasize that such spurious timeouts should be detected and the RTO recovery should be modified to utilize the detection information of a LDA to improve TCP's performance in wireless networks.