A coverage type generalizes refinement types found in many functional languages with support for \emph{must}-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful as they allow us to verify the \emph{completeness}, as well as safety, of test generators. There is a surprising connection between the kind of underapproximate reasoning coverage types offer and the style of reasoning enabled by recently proposed Incorrectness Logic frameworks. In our presentation, we propose to explore this connection more deeply, identifying mechanisms that more systematically integrate incorrectness reasoning within an expressive refinement type system and the opportunities that such integration offers to functional programmers, program verifiers, and program analyzers and related tools.