In Australia, as elsewhere, household electricity infrastructure is changing: over one-fifth of Australian households have rooftop solar photovoltaics (PV), and there is growing opportunity to purchase household battery storage. Australia has the highest proportion of distributed (household-level) solar PV worldwide. There is, however, concern from Australian utilities and governments that increasing numbers of households will opt to leave the centralised electricity grid, as it becomes technically feasible and cost-effective for them to do so. In this paper we explore the motivations and decision making of off-grid households, through a case study of the State of Tasmania, Australia. Our empirical research involved identifying existing sources of off-grid data and undertaking a survey and interviews of off-grid households. We conceptualise off-grid households as an instance of scarce data – a contrast to the concept of big data. Drawing on insights from critical data studies, we show how scarce data can act as a barrier to effective governance, with energy policy making skewed towards governing data-rich policy areas.