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A sender-receiver paradigm, in which a master and slave node exchange timing packets to estimate the clock offsets of the slave node and other nodes located in the common broadcast region of master and slave nodes, is adopted herein for synchronizing the clocks of individual nodes in a wireless sensor network (WSN). The maximum likelihood estimate of the clock offset of the listening node hearing the broadcasts from both the master and slave nodes was derived, assuming symmetric exponential link delays. This paper advances those results in two directions. First, some improved estimators, each being optimal in its own class, are derived for the clock offset of the listening node and mean link delays. Second, the results are generalized by addressing the more realistic problem of clock offset estimation under asymmetric exponential delays. The results presented in this paper are important for time synchronization of WSNs, where these techniques can be utilized to achieve accurate clock estimates with reduced power consumption.