It is often recognised that in real-life decision situations, classical utility theory puts too strong requirements on the decision-maker. Various interval approaches for decision making have therefore been developed and these have been reasonably successful. However, a problem that sometimes appears in real-life situations is that the result of an evaluation still has an uncertainty about which alternative is to prefer. This is due to expected utility overlaps rendering discrimination more difficult. In this article we discuss how adding second-order information may increase a decision-maker�s understanding of a decision situation when handling aggregations of imprecise representations, as is the case in decision trees or influence diagrams.