The "LFK" index has been promoted as an improved method to detect bias in meta-analysis. Putatively, its performance does not depend on the number of studies in the meta-analysis. We conducted a simulation study, comparing the "LFK" index test to three standard tests for funnel plot asymmetry in settings with smaller or larger group sample sizes. In general, false positive rates of the "LFK" index test markedly depended on the number and size of studies as well as the between-study heterogeneity with values between 0% and almost 30%. Egger's test adhered well to the pre-specified significance level of 5% under homogeneity, but was too liberal (smaller groups) or conservative (larger groups) under heterogeneity. The rank test was too conservative for most simulation scenarios. The Thompson-Sharp test was too conservative under homogeneity, but adhered well to the significance level in case of heterogeneity. The true positive rate of the "LFK" index test was only larger compared with classic tests if the false positive rate was inflated. The power of classic tests was similar or larger than the "LFK" index test if the false positive rate of the "LFK" index test was used as significance level for the classic tests. Under ideal conditions, the false positive rate of the "LFK" index test markedly and unpredictably depends on the number and sample size of studies as well as the extent of between-study heterogeneity. The "LFK" index test in its current implementation should not be used to assess funnel plot asymmetry in meta-analysis.