Results of clinical trials are often combined in a meta-analysis using the random-effects model. Despite its theoretical advantages the model is often criticised for being overly sensitive to various sources of bias. From a modelling perspective such shortcomings may be fixed by incorporating uncertainty of the between-study variance estimate. This technique is, however, has not yet been tested rigorously. We conduct a comprehensive simulation study to compare meta-analytic inferences from the random-effects model with and without incorporating uncertainty of the between-study variance estimate. Our results strongly suggest that incorporating uncertainty of the between-study variance estimate in the random-effects model will reduce bias of pooled treatment effects, reduce type I error, and improve the coverage of confidence intervals in biased meta-analyses.