Influenza is an important cause of mortality in temperate countries, but there is substantial controversy as to the total direct and indirect mortality burden imposed by influenza viruses. The authors have extracted multiple-cause death data from public-use data files for the United States from 1979 to 2001. The current research reevaluates attribution of deaths to influenza, by use of an annualized regression approach: comparing measures of excess deaths with measures of influenza virus prevalence by subtype over entire influenza seasons and attributing deaths to influenza by a regression model. This approach is more conservative in its assumptions than is earlier work, which used weekly regression models, or models based on fitting baselines, but it produces results consistent with these other methods, supporting the conclusion that influenza is an important cause of seasonal excess deaths. The regression model attributes an annual average of 41,400 (95% confidence interval: 27,100, 55,700) deaths to influenza over the period 1979-2001. The study also uses regional death data to investigate the effects of cold weather on annualized excess deaths.