Ansatz for small FCNC with a non-universal $Z^\prime$

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 $V_{ts}$.