Many authors conducting meta-analyses struggle with the decision of choosing between the fixed-effect and random-effects models. The models possess different pros and cons and may yield contradicting results. There is a need for a more reliable approach that adopts the pros and minimises the cons of both models. Biggerstaff & Tweedie proposed a method to calculate the weights in random-effects meta-analyses that incorporates the variability of the between-study variance estimate. Presumably this method lets the fixed- and random-effects models 'meet in the middle'. To examine this issue we performed a simulation study. We based our simulations on the data from six heterogeneous meta-analyses that included at least thirty trials and had converged to approximately equal fixed- and random-effects pooled estimates. We accepted the pooled estimates of the original meta-analyses as our 'gold standard'. We simulated cumulative meta-analyses including a large number of trials. We calculated the ratios between the simulated, cumulative estimates and the 'gold standard' estimates. We obtained the median (50% quantile) to measure accuracy, and the 2.5% and 97.5% quantiles to measure the precision of the simulated, cumulative point estimates. We also determined the coverage that each of the simulated, cumulative estimates' 95% confidence intervals provided. Cumulative estimates were recorded five times throughout each simulated meta-analysis to indicate meta-analysis updates. We compared accuracy, precision, and coverage of the fixed-effect model, the random-effects model, and the Biggerstaff & Tweedie method after the first simulated yielding statistical significance and after each of the simulated updates. Our study suggests that the Biggerstaff and Tweedie random-effects method generally attains high point estimate precision, adopts the higher accuracy of the fixed-effect model, and adopts the higher coverage of the random-effects model. Our findings, however, need confirmation from other simulation studies as well as motivating examples.