Recent literature has examined the problem facing decisionmakers with bounded awareness, who may be unaware of some states of nature. A question that naturally arises here is whether a value of awareness (VOA), analogous to VOI, can be attributed to changes in awareness. In this note it is shown, in a sense that will be made precise, that the sum VOA+VOI is constant and independent of the choice set. It follows that, the greater is VOA, the less is VOI. This point is illustrated for a simple two-state case, then proved for general classes of choice sets. The analysis is then extended to cover alternative concepts of choice under unawareness.