Starting from a model of ZFC with two supercompact cardinals, I will discuss how to force and construct a model in which the first two strongly compact cardinals κ₁ and κ₂ are also the first two measurable cardinals. In this model, κ₁'s strong compactness is indestructible under arbitrary κ₁-directed closed forcing, and κ₂'s strong compactness is indestructible under Add(κ₂, λ) for any ordinal λ. This answers a generalized version of a question of Sargsyan.