A number of studies have recently shown an association between particle concentrations in outdoor air and daily mortality counts in urban locations. In the public health interpretation of this evidence, a key issue is whether the increased mortality associated with higher pollution levels is restricted to very frail persons for whom life expectancy is short in the absence of pollution. This possibility has been termed the "harvesting hypothesis." We present an approach to estimating the association between pollution and mortality from times series data that is resistant to short-term harvesting. The method is based in the concept that harvesting alone creates associations only at shorter time scales. We use frequency domain log-linear regression to decompose the information about the pollution-mortality association into distinct time scales, and we then create harvesting-resistant estimates by excluding the short-term information that is affected by harvesting. We illustrate the methods with total suspended particles and mortality counts from Philadelphia for 1974-1988. The total suspended particles-mortality association in Philadelphia is inconsistent with the harvesting-only hypothesis, and the harvesting-resistant estimates of the total suspended particles relative risk are actually larger-not smaller-than the ordinary estimates.