Composite indices have been prominently used in poverty research. However, validity of these indices remains subject to debate. This paper examines the validity of a common type of composite poverty indices using data from a cross-sectional survey of 2477 households in urban and rural KwaZulu-Natal, South Africa. Multiple-group comparisons in structural equation modelling were employed for testing differences in the measurement model across urban and rural groups. The analysis revealed substantial variations between urban and rural respondents both in the conceptualisation of poverty as well as in the weights and importance assigned to individual poverty indicators. The validity of a 'one size fits all' measurement model can therefore not be confirmed. In consequence, it becomes virtually impossible to determine a household's poverty level relative to the full sample. Findings from our analysis have important practical implications in nuancing how we can sensitively use composite poverty indices to identify poor people.