  We explore models with additional right-handed gauge bosons that couple
predominantly to the third generation in the context of $b\bar{b}$ production
at LEP. In particular we investigate potential new contributions to $\delta
g_{Rb}$ that are needed if the measured $A^b_{FB}$ at the $Z$ peak is
interpreted as a signal of new physics. We identify two sources of large
$\delta g_{Rb}$ corrections: $Z-Z^\prime$ mixing at tree-level, and one-loop
effects from a new $SU_R(2)$ triplet of gauge bosons. We find that the latter
can contribute to $\delta g_{Rb}$ at the 1%-level. We place bounds on the mass
of the additional $Z^\prime$ gauge boson that occurs in these models using the
$R_b$ measurements from LEP-II. We find that even in cases where the $Z^\prime$
couples almost exclusively to the $b$ and $t$-quarks, masses lighter than about
500 GeV are already excluded.
