 The flip side of hyperintensionality’s pervasiveness is its encompassing very diverse phenomena. We now investigate what (little) we know about the general structure of hyperintensionality. The initial characterization, recall, merely tells us that a concept or operator is hyperintensional when it is more fine-grained than intensional or standard modal concepts or operators, marking a distinction invisible to the latter. As Jespersen and Duží reminded us, little is said on “how hyper” hyperintensions are. The tag of “granularity problems” (Barwise 1997; Jago 2014; Bjerring &amp; Schwarz 2017) labels a set of issues concerning the right level of fine-grainedness. There are several related problems here, because different hyperintensional concepts seem to display different degrees of fine-grainedness. This can be understood again in terms of substitution salva veritate for the relevant operators: \(X\) is strictly more fine-grained than \(Y\) when all substitutions that go through for \(X\) also do for \(Y,\) but \(X\) fails some, which goes through for \(Y.\)