Opportunities to decrease the toxicity and cost of approved treatment regimens with lower dose, less frequent, or shorter duration alternative regimens have been limited by the perception that alternatives must be non-inferior to approved regimens. Non-inferiority trials are large and expensive to do, because they must show statistically that the alternative and approved therapies differ in a single outcome, by a margin far smaller than that required to demonstrate superiority. Non-inferiority's flaws are manifest: it ignores variability expected to occur with repeated evaluation of the approved therapy, fails to recognise that a trial of similar design will be labelled as superiority or non-inferiority depending on whether it is done prior to or after initial registration of the approved treatment, and relegates endpoints such as toxicity and cost. For example, while a less toxic and less costly regimen of 3 months duration would typically be required to demonstrate efficacy that is non-inferior to that of a standard regimen of 6 months to displace it, the longer duration therapy has no such obligation to prove its superiority. This situation is the tyranny of the non-inferiority trial: its statistics perpetuate less cost-effective regimens, which are not patient-centred, even when less intensive therapies confer survival benefits nearly identical to those of the standard, by placing a disproportionately large burden of proof on the alternative. This approach is illogical. We propose that the designation of trials as superiority or non-inferiority be abandoned, and that randomised, controlled trials should henceforth be described simply as "comparative".