Despite its ad hoc nature and lack of an appealing economic interpretation, the critical cost-efficiency index (or CCEI) proposed in Afriat (1973) is one of the most widespread measures of departures from rationality. In this paper, we provide a behavioural foundation for this index by showing that it is equivalent to a notion of the just-noticeable difference — a measure of dissimilarity between alternatives that is sufficient for the agent to tell them apart.