The use of approximate unconditional P-values is examined in the sign test with ties and the 2 2 matched-pairs trial. These P-values are calculated using a simple bootstrap plug-in rule, which requires no Monte Carlo and can be iterated an arbitrary number of times. Certain of these P-values yield corresponding tests of hypotheses which are very nearly exact and have considerably higher unconditional power than the usual exact conditional test. They can also be expected to have higher power than competing exact unconditional tests and are easier to compute.