The standard version of the psychological criterion or theory of personal identity takes it that psychological connectedness is not necessary for personal identity, or for what matters in survival. That is, a future person can be you, and/or have what matters in survival for you, even though there is no psychological connectedness between you and that future person. David Lewis, however, holds that psychological connectedness is necessary to both identity and what matters (which he takes to coincide). This entails, Lewis acknowledges, that if a human body were to live longer than connectedness lasts, then that body would ‘embody’ or ‘constitute’ a different person later on than it did to begin with. Moreover, Lewis accepts, a body may embody more than one person at any one time. Lewis claims that this can be reconciled to some degree with common sense if we count by person stages rather than by persons. I show, though, that Lewis' view cannot be salvaged in this way, and, moreover, that it leads to further absurdities. I conclude that as an account of identity and of what matters in survival, it is highly implausible, and most unsatisfactory.