The extinction of small populations is a stochastic process, affected by both environmental variation and chance variation in the fates of individuals (demographic stochasticity). Here I examine how population extinction risk is affected by variation in the underlying individual phenotypes, using a branching-process approach. I define the long-term individual extinction risk as the chance of ultimately leaving no descendants, and the cumulative individual extinction risk as the chance of leaving no descendants by a specified time. I use these to show that if there is a phenotypic correlation between parents and their offspring, variation in these quantities always reduces both the long- and short-term population extinction risk. Such variation in individual extinction risk arises from individual variation in demographic parameters and may have both genetic and environmental causes. Using a well-known approximation of the difference between the log arithmetic and log geometric means, I derive expressions for the sensitivity and elasticity of the approximate log extinction risk to changes in the mean and variance of the individual extinction risk, and to changes in population size. One conclusion is that increasing the variance among individuals in extinction risk can sometimes be at least as important in reducing population extinction risk as increasing the population size itself. These analyses also point to reasons why changes in environmental factors (e.g., toxicants) or management practices may have either larger or smaller effects than would be anticipated by considering the change in the mean risk alone.