  We consider the electroweak theory with an additional neutral vector boson
$Z^\prime$ at one loop. We propose a renormalization scheme which makes the
decoupling of heavy $Z^\prime$ effects manifest. The proposed scheme justifies
the usual procedure of performing fits to the electroweak data by combining the
full SM loop corrections to observables with the tree level corrections due to
the extended gauge structure. Using this scheme we discuss in the model with
extra an $U(1)^\prime$ group factor 1-loop results for the $\rho$ parameters
defined in several different ways.
