We analyze a 140-year series of smallpox deaths in the Åland Islands, Finland. Vaccination, introduced in 1805, dramatically reduced the annual number of smallpox deaths. It also influenced the age distribution of smallpox deaths, changing smallpox from a childhood disease before 1805 to one which affected both adults and children after 1805. This appears to be due to the fact that Ålanders were usually vaccinated only once during childhood and often lost their immunity during adulthood. Spectral analysis of the prevaccination time series of smallpox deaths demonstrates a strong seven-year periodicity, reflecting the amount of time necessary to build up a cohort of nonimmune individuals. After the introduction of vaccination, the periodicity changes to eight years. The probability that a parish in Åland was affected by a smallpox epidemic is shown to be highly correlated with migration patterns and parish population sizes.