A well known method of estimating the offset between two clocks in a data communication network involves exchanging timing messages between the clocks. Different distributions of the transmission delays in the two directions associated with the exchanged messages cause the estimator to be biased. Bootstrap bias-correction improves the estimator with respect to mean squared error. Studies on network traffic show that no single distribution adequately characterizes delays, and thus robustness of an estimator to different distribution assumptions is a critical property for an estimator to have. For common distribution assumptions for the transmission delays, the bias-corrected estimator has smaller mean squared error than the uncorrected estimator. Recent studies of Internet traffic show that delay distributions can be heavy-tailed. Evaluation of bootstrap bias corrected estimators in the context of heavy tailed network delays leads to some surprising results. Confidence interval procedures for clock offset and a brief discussion of estimating the difference in rates between two clocks will also be given.