Sufficientarian theories of distributive justice are often considered to be vulnerable to the 'blindness to inequality and other values objection'. This objection targets their commitment to holding the moral irrelevance of requirements of justice above absolute thresholds of advantage, making them insufficiently sensitive to egalitarian moral concerns that do have relevance for justice. This paper explores how sufficientarians could reply to this objection. Particularly, I claim that, if we accept that the force of the aforementioned objection comes from relational, and not distributive, inequalities, different strategies are open for sufficientarians in order to be sensitive to these concerns. Drawing on recent literature about the relation between distributive and relational egalitarianism, and the possibility of reducing one to the other, strategies of 'internalizing' and 'externalizing' relational egalitarian concerns to a distributive sufficientarian framework are explored. In turn, I suggest that both strategies fail in their standard versions, but argue that a particular 'hybrid view' about justice is an attractive candidate for the sufficientarian theorist.