NonBayesian approaches to log-linear models depend heavily on asymptotic theory. What is to be done when the sample sizes are not large? Exact conditional tests provide one approach. This methodology seems to have been first introduced by ... who else? R. A. Fisher. We introduced Fisher’s exact test for a \(2\times 2\) table in Exercise 2.7.5 and additional background was given in Sect. 3.5.1 . Agresti (Statistical Science, 7, 131–153 (1992)) reviews not only exact conditional tests but other related forms of inference including confidence intervals. As examined in Agresti’s paper and its discussion, there is substantial debate about the efficacy of these methods. What is not up for debate is the fact that these methods, when they can be computed, provide valid significance tests of the log-linear model being tested. (Significance tests ask only whether the data tend to contradict the null model and involve no explicit alternative model/hypothesis.)