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We improve previous work on the consistency strength of mutually stationarysequences of sets concentrating on points with divergent cofinality building onprevious work by Adolf, Cox and Welch. Specifically, we have greatly reducedour reliance on covering properties in the proof. This will allow us to handlesequences in which sets concentrating on points of countable cofinality appearinfinitely often. Furthermore we will show that if $\kappa$ is a J\'onssoncardinal with $\kappa < \aleph_\kappa$ then the sharp for a model with a strongcardinal exists.

Lower consistency bounds for mutual stationarity with divergent cofinalities and limited covering