Counting process representations are used to study the efficacies of two classes of censored paired data statistics one proposed by Woolson and Lachenbruch (1980) and the other by Popovich and Rao (1985). Expressions for efficacies are derived using contiguous sequences of parametric alternatives. The results are used to determine the form of the statistic with maximum efficacy in each class. Relative efficiencies are evaluated under a log-linear model assuming a variety of values for the correlation coefficient between the log of survival times and for the probability of double censoring. The relative efficiency comparisons indicate that the statistics proposed by Popovich and Rao perform as well as those proposed by Woolson and Lachenbruch. When the probability of double censoring is high. the former statistics have a slight advantage over the other.