This paper examines the implications of the ranking relation generated by two non-intersecting relative deprivation curves as developed in Kakwani (1984). It is shown that the dominance in terms of relative deprivation implies the Lorenz domination, hence welfare improvement property (that is, welfare increases under Pigou-Dalton type progressive income transfers), but the converse is not true. Next, the class of average relative deprivation indices that agrees with the deprivation dominance criterion is identified. It turns out that all such deprivation indices can be regarded as Lorenz consistent inequality indices, but the reverse implication does not follow.