Are theories ‘underdetermined by the evidence’ in any way that should worry the scientiﬁc realist? I argue that no convincing reason has been given for thinking so. A crucial distinction is drawn between data equivalence and empirical equivalence. Duhem showed that it is always possible to produce a data equivalent rival to any accepted scientiﬁc theory. But there is no reason to regard such a rival as equally well empirically supported and hence no threat to realism. Two theories are empirically equivalent if they share all consequences expressed in purely observational vocabulary. This is a much stronger requirement than has hitherto been recognised— two such ‘rival’ theories must in fact agree on many claims that are clearly theoretical in nature. Given this, it is unclear how much of an impact on realism a demonstration that there is always an empirically equivalent ‘rival’ to any accepted theory would have—even if such a demonstration could be produced. Certainly in the case of the version of realism that I defend—structural realism—such a demonstration would have precisely no impact: two empirically equivalent theories are, according to structural realism, cognitively indistinguishable.