We study in this paper two competing TCP connections that share a common bottlerreck link. When congestion occurs, one (or both) connections will suffer a loss that will cause its throughput to decrease by a multiplicative factor. The identity of the connection that will suffer a loss is determined by a randomized "loss strategy" that may depend on the throughputs of the connections at the congestion instant. We analyze several such loss strategies. After deriving some results for the general asymmetric case, we focus in particular on the symmetric case and study the infiuence of the strategy on the average throughput and average utilization of the link. As the intuition says, a strategy that assigns a loss to a connection with a higher throughput is expected to give worse performance since the total instantaneous throughput after a loss is expected to be lower with such a strategy. We show that, surprisingly, the average throughput and average link utilizations are invariant: they are the same under any possible strategy; the link utilization is 6/ 7 of the link capacity. We show, in contrast, that the second moment of the throughput does depend on the strategy.