We propose modified exact inferential methods for contingency tables. Ordinary “exact” inference is conservative, because of the discreteness. For estimating a common odds ratio in several 2 × 2 tables, two modifications of the ordinary “exact” confidence interval maintain at least a fixed confidence level but tend to be much narrower. One approach inverts results of a test with a modifiedPvalue utilizing the test statistic and table probabilities. The second approach inverts one two-sided test rather than two one-sided tests. This approach is much less conservative when the true odds ratio is relatively small or large. We also generalize results of Cohen and Sackrowitz and relate modifiedPvalues to construction of exact, unbiased, and admissible tests for an ordinal alternative to conditional independence.