Using a combination of descriptive and multivariate regression methods applied on a sample survey (n=4000) conducted in Luhansk (Ukraine) during Fall 2013, this paper investigates demographic, socio-economic, housing-specific and geographical factors that predict urban poverty in countries undergoing economic, political and institutional transition from state socialism to the market with a specific focus on Ukraine. By doing so, it contributes to the literature on poverty under and after transition, which has a strong position within economics, and to the literature on the spatial expressions of poverty after state socialism, which is particularly prominent within geography. Inspired by Amartya Sen's notion that poverty contains an irreducible absolute core, as well as a relative component, this paper makes use of a poverty index based on multiple thresholds that reflect the respondents' capabilities to meet different needs. A fascinating result of this exercise is that poverty under transition is not only predicted by such classical factors as sex, personal and parental education, and socio-occupational status, but also by housing-specific details such as location in vertical space and by classical geographical factors such as relative horizontal location and neighborhood prestige. Accordingly, this paper responds to recent calls for increased sensitivity towards the third dimension of space in contemporary urbanism, while at the same time making a substantial contribution to our hitherto incomplete knowledge of the patterns and sources of urban poverty and inequality in postsocialist transition.