Australia's economy and labour market have escaped a dramatic downturn following the global financial economic crisis. Yet, a substantial share of working-age Australians either were not working or worked only to a limited extent as the global recovery gathered pace between 2013 and 2014. 18% were without employment during an entire year; a further 6% had weak labour-market attachment, e.g. working only a fraction of the year. This paper extends a method proposed by Fernandez et al. (2016) to measure and visualise employment barriers of individuals with weak labour-market attachment using household micro-data. It first develops indicators to quantify employment obstacles under three headings: (i) work-related capabilities, (ii) incentives, and (iii) employment opportunities. A novelty in this paper is a statistical procedure for calibrating the definition of barriers in a way that maximises their explanatory power in predicting employment outcomes. A statistical clustering algorithm then identify groups with similar combinations of barriers. The resulting typology provides insights on the most pressing policy priorities in supporting different groups into employment in Australia. We identify seven distinct groups, each calling for a specific flavour of activation and employment-support policies. The most common employment obstacles are limited work experience, low skills and poor health. Financial disincentives, care responsibilities and scarce job opportunities are less widespread overall but were important barriers for some groups. Almost one third of jobless or low-intensity workers face three or more simultaneous barriers, highlighting the limits of policy approaches that focus on subsets of these employment obstacles in isolation.