 Third, the argument is not best understood as the claim that, if one does not accept transworld identities, then one is forced into denying the Barcan scheme (and hence forced into uncomfortable logical territory). That claim would be true only if the Barcan scheme were validated only by constant-domain semantics, which is not the case. Counterpart-theoretic semantics can be restricted so as to validate the Barcan scheme, by insisting that the counterpart relation is an equivalence relation which, for each particular x and world w, relates x to a unique particular in w. (One could not then interpret the counterpart relation in terms of similarity, as Lewis does.) Rather, the argument should be understood as the claim that the best way to gain the advantages of a logic containing the Barcan scheme is by adopting constant-domain semantics (and genuine transworld identities along with it). But just which metaphysical view counts as ‘best’ here will involve a trade-off between many factors. These include the simplicity of the constant-domain semantics, on the one hand, but also arguments of the kind raised by Lewis against modal realism with overlap, on the other.