We assess individuals' preferences for time paths of reductions in mortality risk yielding a life-expectancy gain of about one month. In a survey of more than 1000 French residents, we find substantial coherence and heterogeneity. We elicit pairwise preferences between three perturbations of age- and gender-specific survival curves: transient (reduce hazard for next ten years), additive (reduce hazard in all future years by subtracting a constant), and proportional (reduce hazard in all future years by a common fraction). The preference order implied by these pairwise responses is transitive for 85 percent of respondents. The most common preference orders, accounting for more than half the respondents, are strict indifference, proportional ≻ additive ≻ transient, and the inverse of that ranking. These are consistent with globally risk-neutral, risk-seeking, and risk-averse preferences toward longevity, respectively. Choices between one of these scenarios and a latent version that provides no risk reduction for the first 10 or 20 years are consistent with these risk postures. The mean and median consumption-discount rate are 12 and 5 percent per year, respectively, and the average coefficient of relative risk aversion with respect to financial gambles is about 0.5. Preferences toward the time path of mortality-risk reduction are not strongly associated with individual characteristics, although respondents who are older or exhibit higher consumption-discount rates tend to exhibit less longevity-risk aversion.