Monitoring ongoing clinical trials for early signs of effectiveness is an option for improving cost-effectiveness of trials that is becoming increasingly common. Alongside the obvious advantages made possible by monitoring, however, there are some downsides. In particular, there is growing concern in the medical community that trials stopped early for benefit tend to overestimate treatment effect. In this paper, I examine this problem from the point of view of statistical methodology, starting from the observation that the overestimation is caused by (...) the statistical method adopted. Consequently, I argue that some modifications can and should be made to the present statistical framework in order not to miss the advantages the possibility of monitoring can grant. (shrink)