  We study the discovery potential of the Tevatron for a Z-prime gauge boson.
We introduce a parametrization of the Z-prime signal which provides a
convenient bridge between collider searches and specific Z-prime models. The
cross section for p pbar -> Z-prime X -> l^+ l^- X depends primarily on the
Z-prime mass and the Z-prime decay branching fraction into leptons times the
average square coupling to up and down quarks. If the quark and lepton masses
are generated as in the standard model, then the Z-prime bosons accessible at
the Tevatron must couple to fermions proportionally to a linear combination of
baryon and lepton numbers in order to avoid the limits on Z--Z-prime mixing.
More generally, we present several families of U(1) extensions of the standard
model that include as special cases many of the Z-prime models discussed in the
literature. Typically, the CDF and D0 experiments are expected to probe
Z-prime-fermion couplings down to 0.1 for Z-prime masses in the 500--800 GeV
range, which in various models would substantially improve the limits set by
the LEP experiments.
