Randomised trials can provide excellent evidence of treatment benefit in medicine. Over the last 50 years, they have been cemented in the regulatory requirements for the approval of new treatments. Randomised trials make up a large and seemingly high-quality proportion of the medical evidence-base. However, it has also been acknowledged that a distorted evidence-base places a severe limitation on the practice of evidence-based medicine (EBM). We describe four important ways in which the evidence from randomised trials is limited or partial: the problem of applying results, the problem of bias in the conduct of randomised trials, the problem of conducting the wrong trials and the problem of conducting the right trials the wrong way. These problems are not intrinsic to the method of randomised trials or the EBM philosophy of evidence; nevertheless, they are genuine problems that undermine the evidence that randomised trials provide for decision-making and therefore undermine EBM in practice. Finally, we discuss the social dimensions of these problems and how they highlight the indispensable role of judgement when generating and using evidence for medicine. This is the paradox of randomised trial evidence: the trials open up expert judgment to scrutiny, but this scrutiny in turn requires further expertise.