  The CDF collaboration has set lower limits on the masses of the Z' bosons
occurring in a range of E_6 GUT based models. We revisit their analysis and
extend it to certain other E_6 scenarios as well as to some general classes of
models satisfying the anomaly cancellation conditions, which are not included
in the CDF analysis. We also suggest a Bayesian statistical method for finding
exclusion limits on the Z' mass, which allows one to explore a wide range of
the U(1)' gauge coupling parameter. This method also takes into account the
effects of interference between the Z' and the SM gauge bosons.
