The enduring replication crisis in many scientific disciplines casts doubt on the ability of science to estimate effect sizes accurately, and in a wider sense, to self-correct its findings and to produce reliable knowledge. We investigate the merits of a particular countermeasure-replacing null hypothesis significance testing (NHST) with Bayesian inference-in the context of the meta-analytic aggregation of effect sizes. In particular, we elaborate on the advantages of this Bayesian reform proposal under conditions of publication bias and other methodological imperfections that are typical of experimental research in the behavioral sciences. Moving to Bayesian statistics would not solve the replication crisis single-handedly. However, the move would eliminate important sources of effect size overestimation for the conditions we study.