If a trial is adequately powered for two clinically important endpoints, A and B, each of which can fully characterize a treatment benefit to support a regulatory claim by itself, then both endpoints are usually labeled primary, and the trial is deemed positive if either endpoint is statistically significant after a multiplicity adjustment. However, if only A is adequately powered, then should B be designated a secondary endpoint, or should it be retained in the primary family despite being (potentially) underpowered? The former option can lead to a negative trial if A is not statistically significant, no matter how positive the results are for B, since no familywise type I error rate (FWER) is allocated to B, while the latter can reduce the likelihood of a positive trial if an inefficient multiplicity adjustment is used. We underscore this contemporary problem with real examples and offer a novel and intuitively appealing solution for accommodating clinically important but potentially underpowered endpoint(s) in the primary family. In our proposal, for the above scenario with two endpoints, A is tested at a prespecified level α₁=α−ε (e.g. ε=0.01 when α=0.05), and B at an ‘adaptive’ level α₂ (⩽α) calculated using a prespecified non‐increasing function of the p‐value for A. Our method controls the FWER at level α and can notably increase the probability of achieving a positive trial compared with a fixed prospective alpha allocation scheme (Control. Clin. Trials 2000; 20:40–49), and with Hochberg's method applied to the family of primary endpoints. Importantly, our proposal enables strong results for potentially underpowered primary endpoint(s) to be interpreted in a conclusive rather than exploratory light. Copyright © 2008 John Wiley & Sons, Ltd.