The authors postulate a family-based poverty index (JD) possessing focus, symmetry, monotonicity and decomposability properties commonly required of individualistic indexes. JD also satisfies reformulated distribution and transfer sensitivity axioms which take account of differences between families in their sizes and poverty lines. The authors introduce a new axiom, substitution sensitivity, which is satisfied by JD but not by the well-known FGT index. Using JD, they describe Australian poverty in the 1980s. The authors find that head-count ratios and average income gaps dominate the explanation of differences in poverty across family types and across time. Differences in the distributions of poor incomes make minor contributions. Copyright 1999 by The Economic Society of Australia.