Summary: Starting from a supercompact cardinal \(\kappa \), we force and construct a model in which \(\kappa \) is both the least strongly compact and least supercompact cardinal and \(\kappa \) exhibits mixed levels of indestructibility. Specifically, \(\kappa \)'s strong compactness, but not its supercompactness, is indestructible under any \(\kappa \)-directed closed forcing which also adds a Cohen subset of \(\kappa \). On the other hand, in this model, \(\kappa \)'s supercompactness is indestructible under any \(\kappa \)-directed closed forcing which does not add a Cohen subset of \(\kappa \).