In random-effects meta-analysis the between-study variance (tau(2) ) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating tau(2) and the overall effect and produce confidence intervals with below-nominal coverage. An improved approximation to the moments of Cochran's Q statistic, suggested by Kulinskaya and Dollinger, yields new point and interval estimators (KD) of tau(2) and of the overall log-odds-ratio. Another, simpler approach (SSW) uses weights based only on study-level sample sizes to estimate the overall effect. In extensive simulations we compare our proposed estimators with established point and interval estimators for tau(2) and point and interval estimators for the overall log-odds-ratio (including the Hartung-Knapp-Sidik-Jonkman interval). Additional simulations included three estimators based on generalized linear mixed models and the Mantel-Haenszel fixed-effect estimator. Results of our simulations show that no single point estimator of tau(2) can be recommended exclusively, but Mandel-Paule and KD provide better choices for small and large K, respectively. The KD estimator provides reliable coverage of tau(2) . Inverse-variance-weighted estimators of the overall effect are substantially biased, as are the Mantel-Haenszel odds-ratio and the estimators from the generalized linear mixed models. The SSW estimator of the overall effect and a related confidence interval provide reliable point and interval estimation of the overall log-odds-ratio.