We show that gauge invariant extensions of the local functional O = (1)/(2) integrald(4) x A(2) have long range non-localities which can only be "renormalised" with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modem sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature. (C) 2004 Elsevier B.V. All rights reserved.