Cost-effectiveness analysis is usually based on life-years gained estimated from all-cause mortality. When an intervention affects only a few causes of death accounting for a small fraction of all deaths, this approach may lack precision. We develop a novel technique for cost-effectiveness analysis when life-years gained are estimated from cause-specific mortality, allowing for competing causes of death. In the context of randomised trial data, we adjust for other-cause mortality combined across randomised groups. This method yields a greater precision than analysis based on total mortality, and we show application to life-years gained, quality-adjusted life-years gained, incremental costs, and cost effectiveness. In multi-state health economic models, however, mortality from competing causes is commonly derived from national statistics and is assumed to be known and equal across intervention groups. In such models, our method based on cause-specific mortality and standard methods using total mortality give essentially identical estimates and precision. The methods are applied to a randomised trial and a health economic model, both of screening for abdominal aortic aneurysm. A gain in precision for cost-effectiveness estimates is clearly helpful for decision making, but it is important to ensure that 'cause-specific mortality' is defined to include all causes of death potentially affected by the intervention.