This paper shows that the two most devastating objections to Shogenji's formal account of coherence necessarily involve information sets of cardinality n>2. Given this, it is surmised that the problem with Shogenji's measure has more to do with his means of generalizing the measure than with the measure itself. The author defends this claim by offering an alternative generalization of Shogenji's measure. This alternative retains the intuitive merits of the original measure while avoiding both of the relevant problems that befall it. In the light of all of this, he suggests that there is new hope for Shogenji's analysis: Shogenji's early and influential attempt at measuring coherence, when generalized in a subset-sensitive way, is able to clear its most troubling objections.