  We revisit the CDF data on di-muon production to impose constraints on a
large class of Z' bosons occurring in a variety of E_6 GUT based models. We
analyze the dependence of these limits on various factors contributing to the
production cross-section, showing that currently systematic and theoretical
uncertainties play a relatively minor role. Driven by this observation, we
emphasize the use of the Bayesian statistical method, which allows us to
straightforwardly (i) vary the gauge coupling strength, g', of the underlying
U(1)'; (ii) include interference effects with the Z' amplitude (which are
especially important for large g'); (iii) smoothly vary the U(1)' charges; (iv)
combine these data with the electroweak precision constraints as well as with
other observables obtained from colliders such as LEP 2 and the LHC; and (v)
find preferred regions in parameter space once an excess is seen. We adopt this
method as a complementary approach for a couple of sample models and find
limits on the Z' mass, generally differing by only a few percent from the
corresponding CDF ones when we follow their approach. Another general result is
that the interference effects are quite relevant if one aims at discriminating
between models. Finally, the Bayesian approach frees us of any ad hoc
assumptions about the number of events needed to constitute a signal or
exclusion limit for various actual and hypothetical reference energies and
luminosities at the Tevatron and the LHC.
