During patient follow-up in a randomized trial, some deaths may occur. Where death (or noncardiovascular death) is not part of an outcome of interest it is termed a competing risk. Conventional analyses (eg, Cox proportional hazards model) handle death similarly to other censored follow-up. Patients still alive are unrealistically assumed to be representative of those who died. The Fine and Gray model has been used to handle competing risks, but is often used inappropriately and can be misleading. We propose an alternative multiple imputation approach that plausibly accounts for the fact that patients who die tend also to be at high risk for the (unobserved) outcome of interest. This provides a logical framework for exploring the impact of a competing risk, recognizing that there is no unique solution. We illustrate these issues in 3 cardiovascular trials and in simulation studies. We conclude with practical recommendations for handling competing risks in future trials.