Despite the formal rigour that attends social and economic measurement, the substantive meaning of particular measures could be compromised in the absence of a clear and coherent conceptualization of the phenomenon being measured. A case in point is afforded by the status of a ‘focus axiom’ in the measurement of poverty. ‘Focus’ requires that a measure of poverty ought to be sensitive only to changes in the income-distribution of the poor population of any society. In practice, most poverty indices advanced in the literature satisfy an ‘income-focus’ but not a ‘population-focus’ axiom. This, it is argued in the present paper, makes for an incoherent underlying conception of poverty. The paper provides examples of poverty measures which either satisfy both income and population focus or violate both, or which effectively do not recognize a clear dichotomization of a population into its poor and non-poor components, and suggests that such measures possess a virtue of consistency, and coherent meaning, lacking in most extant measures of poverty available in the literature.Paper submitted to the special issue The Measurement of Inequality and Well-Being: New Perspectives