We present the findings of a new time-series model that estimates short-term health effects of particulate matter and ozone, as applied to three U.S. cities. The model is based on observed fluctuations of daily death counts and estimates the corresponding daily subpopulations at-risk of imminent death; it also shows that virtually all elderly deaths are preceded by a brief period of extreme frailty. We augment previous research by allowing new entrants to this at-risk population to be influenced by the environment, rather than be random. The mean frail subpopulations in the three cities, each containing between 3000 and 5000 daily observations on mortality, pollution, and temperature, are estimated to be about 0.1% of those aged 65 or more, and their life expectancies in this frail status are about one week. We find losses in life expectancy due to air pollution and temperature to be at most one day. Air pollution effects on new entrants into the frail population tend to exceed those on mortality. Our results provide context to the many time-series studies that have found significant short-term relationships between air quality and survival, and they suggest that benefits of air quality improvement should be based on increased life expectancy rather than estimated numbers of excess deaths.