Investigators often design clinical trials without knowing precisely the values of such necessary parameters as the variances or the event rates in the control group. In order to determine reasonable values for such parameters, they may design a small pilot study external to the main trial. In this paper we propose designs, which we term internal pilot studies, that designate a portion of the main trial as a pilot phase. At the end of the internal pilot study, the investigators recompute preselected parameters and recalculate required sample size. The study then proceeds with the modifications dictated by the internal pilot. Final analyses of the results incorporate all data, disregarding the fact that part of the data came from a pilot phase. As one example of this type of design, we consider a study to compare two normally distributed means. By simulation, we show a numerical example for which the effect of the procedure on the alpha-level is negligible, but the potential gain in power considerable. We urge considering a similar approach for a number of types of endpoints.