Although many studies have shown that airborne particles are associated with increased daily death and hospitalization rates, some have questioned whether these events are occurring in persons who would die or enter the hospital within a few days in any case. This hypothesis is usually called the harvesting effect. Harvesting is postulated to occur because the size of the pool of susceptibles decreases as a result of air pollution. I have developed a framework for examining this hypothesis. I used a smoothing technique that allowed me to examine the association between daily deaths and daily hospital admissions net of any such rebound that occurred within a fixed time scale. By varying that time scale I could look at effects net of rebounds on successively larger time scales, ranging from 15 to 60 days. I examined daily deaths and hospital admissions in Chicago for the years 1988-1993. In baseline analyses, particulate matter less than 10 microm in aerodynamic diameter (PM10) was associated with increased daily deaths and hospital admissions for heart disease, pneumonia, and chronic obstructive pulmonary disease. A 10 microg/m3 increase in PM10 was associated with a 0.89% increase in daily deaths (95% confidence interval = 0.61-1.16%), for example. Using smoothing to look at effects net of short-term rebounds, the effect-size estimates for daily deaths and for chronic obstructive pulmonary disease admissions more than doubled. They did not change for pneumonia and heart disease admissions. The increased effect size for daily deaths occurred only for deaths outside of the hospital. These results are consistent with air pollution increasing the size of the risk pool and for most of the deaths being advanced by months to years.