This paper reviews several tests for censored paired data and uses Monte Carlo methods to evaluate their sizes and powers. Each of the tests maintains its size. The Akritas test and the paired Prentice-Wilcoxon test are somewhat more powerful than the Gehan statistic or the generalized signed rank test for most of the distributions studied. If the survival times follow an exponential distribution, then the Gehan and the generalized signed rank tests are more powerful against a location shift alternative.