In order to understand whether a reduction in overall poverty has improved the situations of the poorest, it is crucial to distinguish them from the moderately poor population. In this paper, we explore the mechanisms to distinguish subsets of the poor in a multidimensional counting framework. We examine two approaches that capture two distinct forms of stringent multidimensional poverty: one uses a more stringent vector of deprivation cutoffs, and the other, a more stringent cross-dimensional poverty cutoff. To explore the distinction between these two approaches empirically, we examine the evolution of multidimensional poverty in Nepal. Our findings show crucial differences between these approaches.