African poverty statistics depend on household-level measurements from survey data, making the definition of household of critical importance. Detailed case studies from Tanzania and Burkina Faso explore (1) understandings of household membership and ambiguities, and (2) how well survey definitions capture households as economic units, and the implications for household size and responses to and mitigation of poverty. We develop an analytic framework of ‘open’ and ‘closed’ households. ‘Open’ households cope with poverty using flexibility, movement and extra-household networks, but are poorly represented by survey data. Closed households are likely to be better described by survey data.