Background Clinical trials are challenging in rare diseases like pediatric cancers, where the accrual is limited. In these trials, inference assumptions are the same as in common diseases, that is the sample comes from a quasi-infinite population. This leads to overestimating the variance of the mean treatment effect. The finite-population correction factor correcting this bias is often used in surveys, but not in clinical trials. With few assumptions, the use of this correction factor can improve trials efficiency, showing that the power of those trials is sometimes higher than it appears. Methods First, a simulation study assesses the standard error of the mean treatment effect and coverage of the 95% confidence interval with and without the correction. Second, the analytical power of a z-test with and without the correction is given. Finally, the impact on the sample size calculation is investigated. The impact of assuming a finite population is assessed for varying treatment effect, sample size and population size. Results The simulation results confirm the overestimation of the standard error without the correction factor. When using the correction factor, the gain in power reaches up to 10.1%, 15.3% and 12.3% to detect a difference in treatment effect of 10%, 15% and 20%, respectively. The gain is negligible for n = 30, in scenarios with high power (>95%), and for large populations. This gain in power translates into a decrease in sample size: if the conventional calculation leads to a sample size 10% of the population size, then the sample size can be divided by 1.1; if the conventional calculation leads to a sample size 20% of the population size, then the sample size can be divided by 1.2, in order to reach the planned type I error and power. Conclusion When dealing with rare diseases like pediatric cancers, the power of clinical trials might be higher than it appears if using conventional sample sizes. When correcting the variance of the mean using the population size, a gain in efficiency is observed with reasonable sample sizes and treatment differences for very small population sizes, showing that this approach can be useful for some pediatric cancer clinical trials.