In Vietnam, poverty is prevalent and extremely severe among rural ethnic minorities (REM). Despite a number of studies on characteristics of poverty, very few studies comprehensively examine the determinants of poverty intensity. This study employs binary and fractional logit models to investigate the determinants of poverty and the poverty intensity of the REM. Data are obtained by combining the 2012, 2014, and 2016 Vietnam Household Living Standards Surveys. The results show that education, wage-paying employment, housing conditions, and domestic remittances reduce poverty and its intensity. Poverty incidence reduction also hinges on development programmes on credit and scholarships. The likelihood and shortfall of poverty declined for households residing in the Red River and Mekong Deltas, and in southeast Vietnam. However, language barriers, farm size and overseas remittances influenced the poverty intensity but not the likelihood of poverty. Our results suggest that previous studies using only logit models have neglected several influences of poverty intensity, which the current research overcomes.