  It is well known that a non-universal $Z^\prime$ induces tree-level FCNC
which are severely constrained by experiment, most notably meson mixing. We
point out that there is a class of models, with a down-quark mass matrix of the
Georgi-Jarlskog form, in which the FCNC in the down-type quark sector vanish or
are strongly suppressed. The largest FCNC in these models would occur in the
$tc$ transition with a strength comparable to $V_{ts}$.
