If A and B are C*-algebras with maximal abelian self-adjoint C*-subalgebras (MASAs) C and D, respectively, it is a corollary of a known slice-map result for C*-algebras that the closure C ⊗ D of the algebraic tensor product C ⊙ D in the minimal C*-tensor product A ⊗min B is again a MASA. If k kmax 6= k kmin on A ⊙ B, the situation for the closure of C ⊙ D in A ⊗max B or any other non-minimal C*-completion A ⊗α B of A ⊙ B is less clear. When C has the extension property and B is unital, we show that that C ⊗ D is a MASA in A ⊗α B for any C*-norm α. This result has interesting connections with some long-standing open questions.