In this paper I shall argue that if the Parfitian psychological criterion or theory of personal identity is true, then a good case can be made out to show that the psychological theorist should accept the view I call “psychological sequentialism”. This is the view that a causal connection is not necessary for what matters in survival, as long as certain other conditions are met. I argue this by way of Parfit’s own principle that what matters in survival cannot depend upon a trivial fact.