There is a glaring paradox in all commonly used measures of poverty. The death of a poor person reduces poverty according to these measures. This surely violates our basic intuitions of how poverty measures should behave. It cannot be right in concept that differentially higher mortality among the poor serves to reduce poverty. This paper begins the task of developing poverty measures that are not perversely mortality sensitive. A family of measures is proposed that is an intuitive modification of standard poverty measures to take into account the fact that the rich live longer than the poor.