Under income-differentiated mortality, poverty measures reflect not only the "true" poverty, but, also, the interferences or noise caused by the survival process at work. Such interferences lead to the Mortality Paradox: the worse the survival conditions of the poor are, the lower the measured poverty is. We examine several solutions to avoid that paradox. We identify conditions under which the extension, by means of a fictitious income, of lifetime income profiles of the prematurely dead neutralizes the noise due to differential mortality. Then, to account not only for the "missing" poor, but, also, for the "hidden" poverty (premature death), we use, as a fictitious income, the welfare-neutral income, making indifferent between life continuation and death. The robustness of poverty measures to the extension technique is illustrated with regional Belgian data.