The standard practice in cost-effectiveness analyses of health care is to assign a linear value to increasing lifetime gains. The aim of the current study was to examine the possible existence of non-linear utility for short life extensions. A representative sample of the Norwegian population, aged 40-59 years (n=2402), was asked to imagine that they had a limited remaining lifetime (1 year or 10 years) and were offered a treatment that would increase lifetime by a specified amount of time from 1 week to 1 year. In all scenarios, the price per week of life extension was held constant. The proportion of respondents that accepted the treatment increased with increasing extensions, indicating a convex utility function. The result suggests increasing marginal utility for life extensions up to 1 year.