To minimise bias, clinical trials must be randomised, and all patients analysed by allocated treatment. With several separate randomisations, patients should be analysed only within the randomisation they entered, and not compared against patients in different randomisations. Some people worry that randomised trials result in many patients receiving an inferior treatment. Accordingly, several suggestions have been made, including a combined control arm for many trials, and performing several randomisations at the same up-front time point. These approaches fundamentally contradict the above statistical principles, and can lead to wrong conclusions. We explore these problems, with reference to one such recent proposal.