We consider a three-level meta-analysis of standardized mean differences. The standard method of estimation uses inverse-variance weights and REML/PL estimation of variance components for the random effects. We introduce new moment-based point and interval estimators for the two variance components and related estimators of the overall mean. Similar to traditional analysis of variance, our method is based on two conditional $Q$ statistics with effective-sample-size weights. We study, by simulation, bias and coverage of these new estimators. For comparison, we also study bias and coverage of the REML/PL-based approach as implemented in {\it rma.mv} in {\it metafor}. Our results demonstrate that the new methods are often considerably better and do not have convergence problems, which plague the standard analysis.

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