The market for private life annuities is characterised by adverse selection, that is, contracts offer lower than fair payoffs to individuals with low life expectancy. Moreover, life expectancy and income have been found to be positively correlated. The paper shows that a linear tax on annuity payoffs, which raises more revenues from long-living individuals than from short-living, represents an appropriate instrument for redistribution, in addition to an optimally designed labour income tax. Further, we find that a nonlinear tax on annuity payoffs can be directly employed to correct the distortion of the rate of return caused by asymmetric information. These results are contrasted with theoretical findings concerning the role of a tax on capital income.