We use a statistical model to examine the relationship between alpha level, sample size, trial duration, patient accrual rate and therapeutic innovation rate on the increase in treatment efficacy achieved after a series of two-treatment randomized phase III trials. In a setting where the trials include most of the patients in the target population for inference, as in some paediatric cancers, we show that the traditional criteria by which one determines trial size are difficult to justify and apply. In particular, using as a measure of evidence type I error levels larger than the typical 5 per cent for judging treatment differences, and performing smaller trials than one would usually consider feasible, yields on average, over a 25-year research course, larger gains in cure rate. Judicious choice of type I error rate and trial size keeps the chance of worsening treatment efficacy at a low level, even while increasing the chance of making large improvements in cure rate. We propose that a more appropriate view of trial design in low-incidence cancer settings is in the overall context of the research setting and long-term goals rather than in the narrow context of the current single trial. From this viewpoint, insistence on large trials and stringent evidence for accepting new treatments can be counter-productive, in that likely gains in efficacy of treatment will be smaller over the long term.