Fleurbaey et al. (2003) develop a bounded dominance test to make robust welfare comparisons, which is intermediate between Ebert’s (1999) cardinal dominance criterion—generalized Lorenz dominance applied to household incomes, divided and weighted by an equivalence scale—and Bourguignon’s (1989) ordinal dominance criterion. In this paper, we develop a more complete, but less robust bounded index test, which is intermediate between Ebert’s (1997) cardinal index test—an index applied to household incomes, divided and weighted by the equivalence scale—and a (new) sequential index test—an index applied to household incomes of the most needy only, the most and second most needy only, and so on. We illustrate the power of our test to detect welfare changes in Russia using data of the RLMS-surveys.