In this paper I argue against proposals that the cleft clause in a specificational pseudocleft is the structural predicate rather than the structural subject of the sentence. I claim that when examples with the right semantic content and discourse functions are constructed, it is possible for the cleft clause to undergo subject-auxiliary inversion ("Isn't where he's going San Francisco?") or to undergo raising ("What he's after seems to be her money"). I claim that the copula can be modified by an auxiliary verb ("But what really may be at issue when this comes to term will be deployment of SDI" [an attested example]), and can undergo gapping ("What Jane wants is never to go out, and what Bill wants, never to stay home"). Finally, I offer a new argument that a tag question pronoun corefers with the cleft clause and not the clefeted constituent ("The one they really want to hire is Tom, isn't it?").