This paper considers methods for comparing poverty in two income distributions. We first discuss the concept and usefulness of the Poverty Gap Profile (PGP) for comparing poverty in two populations. Dominance of one PGP over another suggests poverty dominance for a wide class of indices which may be expressed as functionals of the PGP. We then discuss hypotheses that can be used to test poverty dominance in terms of the PGP and introduce and justify a test statistic based on empirical PGP’s where we allow for the poverty line to be estimated. A method for obtaining critical values by simulation is proposed that takes account of estimation of the poverty line. The finite sample properties of the methods are examined in the context of a Monte Carlo simulation study and the methods are illustrated in an assessment of relative consumption poverty in Australia over the period 1988/1989–2009/2010.