  Indirect precision data are used to constrain the masses of possible extra
Z^prime bosons and their mixings with the ordinary Z. We study a variety of
Z^prime bosons as they appear in E_6 and left-right unification models, the
sequential Z boson, and the example of an additional U(1) in a concrete model
from heterotic string theory. In all cases the mixings are severely constrained
(sin theta < 0.01). The lower mass limits are generally of the order of several
hundred GeV and competitive with collider bounds. The exception is the Z_psi
boson, whose vector couplings vanish and whose limits are weaker. The results
change little when the rho parameter is allowed, which corresponds to a
completely arbitrary Higgs sector. On the other hand, in specific models with
minimal Higgs structures the limits are generally pushed into the TeV region.
