Meta-analysis of 2 × 2 tables is common and useful in research topics including analysis of adverse events and survey research data. Fixed-effects inference typically centers on measures of association such as the Cochran-Mantel-Haenszel statistic or Woolf's estimator, but relies on assuming exact homogeneity across studies, which is often unrealistic. By showing that estimators of several widely-used methods have meaningful estimands even in the presence of heterogeneity, we derive improved confidence intervals for them under heterogeneity. These improvements over current methods are illustrated by simulation, and we also study which factors affect the coverage levels. We find that our confidence intervals provide coverage closer to the nominal level when heterogeneity is present, in both small and large-sample settings. The conventional confidence intervals derived under homogeneity are often conservative, though anti-conservative inferences occur in some scenarios. We also apply the proposed methods to a meta-analysis of 19 randomized clinical trials on the effect of sclerotherapy in preventing first bleeding for patients with cirrhosis and esophagogastric varices. Our methods provide a more interpretable approach to meta-analyzing binary data and more accuracy in characterizing the uncertainty of the estimators.