Spatial poverty comparisons are investigated in three African countries using multidimensional indicators of well-being. The work is analogous to the univariate stochastic dominance literature in that it seeks poverty orderings that are robust to the choice of multidimensional poverty lines and indices. In addition, the study seeks to ensure that the comparisons are robust to aggregation procedures for multiple welfare variables. In contrast to earlier work, the methodology applies equally well to what can be defined as union, intersection, and intermediate approaches to dealing with multidimensional indicators of well-being. Furthermore, unlike much of the stochastic dominance literature, this work computes the sampling distributions of the poverty estimators to perform statistical tests of the difference in poverty measures. The methods are applied to two measures of well-being, the log of household expenditures per capita and children's height-forage z scores, using data from the 1988 Ghana Living Standards Study survey, the 1993 National Household Survey in Madagascar, and the 1999 National Household Survey in Uganda. Bivariate poverty comparisons are at odds with univariate comparisons in several interesting ways. Most important, it cannot always be concluded that poverty is lower in urban areas in one region compared with that in rural areas in another, even though univariate comparisons based on household expenditures per capita almost always lead to that conclusion.