We investigate logit confidence intervals for the odds ratio based on the delta method. These intervals are constructed using pseudo-Bayes estimators. The Gart method and Agresti method smooth the observed counts toward the model of equiprobability and independence, respectively. We obtain better coverage probability by smoothing the observed counts toward the pseudo-Bayes estimators in 2$ imes$2 table. We also improve legit confidence intervals in 2$ imes$2$ imes$K tables by generalizing these ideas. Utilizing pseudo-Bayes estimators, we obtain better coverage probability by smoothing the observed counts toward the conditional independence model, no three-factor interaction model and saturated model in 2$ imes$2$ imes$K tables.