This article addresses inversion in an inverse (VSO) language, Niuean, focusing on two issues. First, it has been proposed that in certain types of copular sentences, such as pseudo-cleft constructions (PCCs), the predicate rather than the subject may move into the specifier position of TP. This raises the question of PCCs in a language in which the predicate normally moves there. Such sentences might exhibit their normal inverse order or the inverse of this. The second issue is what constitutes the predicate in a PCC. The headless relative (and not the DP) is usually analyzed as the predicate because, in standard theories of predication, a referential nominal cannot be a predicate. However, in Niuean PCCs, the DP is usually analyzed as the predicate. I propose that it is in fact a reduced headless relative with a null predicate. It becomes clear that there is no special copular inversion: the inversion requirement is taken care of by the general predicate-fronting process. The analysis thus sheds new light on the general nature of copular inversion and allows Niuean PCCs to fall into the standard view of predication theory.