When designing a clinical trial, there is usually some uncertainty about the variability of the primary outcome variable. This may lead to an unnecessarily high or inadequately low sample size. The internal pilot study approach uses data from patients recruited up to an interim stage to re-estimate the variance and to re-calculate the final sample size accordingly. Previously, simulation studies have shown that this methodology may highly improve the chance to obtain a well-powered trial. However, it also turned out that the type I error rate may be inflated by this procedure. We quantify the maximum excess of the type I error rate for normally distributed outcomes. If strict control of the -level is considered to be an important issue, a method is proposed to achieve this when re-calculating the sample size in internal pilot studies. The characteristics of the power distributions are investigated for various sample size adaptation rules and implications are discussed.