Multi‐arm trials are an efficient way of simultaneously testing several experimental treatments against a shared control group. As well as reducing the sample size required compared to running each trial separately, they have important administrative and logistical advantages. There has been debate over whether multi‐arm trials should correct for the fact that multiple null hypotheses are tested within the same experiment. Previous opinions have ranged from no correction is required, to a stringent correction (controlling the probability of making at least one type I error) being needed, with regulators arguing the latter for confirmatory settings. In this article, we propose that controlling the false‐discovery rate (FDR) is a suitable compromise, with an appealing interpretation in multi‐arm clinical trials. We investigate the properties of the different correction methods in terms of the positive and negative predictive value (respectively how confident we are that a recommended treatment is effective and that a non‐recommended treatment is ineffective). The number of arms and proportion of treatments that are truly effective is varied. Controlling the FDR provides good properties. It retains the high positive predictive value of FWER correction in situations where a low proportion of treatments is effective. It also has a good negative predictive value in situations where a high proportion of treatments is effective. In a multi‐arm trial testing distinct treatment arms, we recommend that sponsors and trialists consider use of the FDR.