  We assume the latest experimental determination of the weak charge of atomic
cesium and analyze its implications for possible new physics. We notice that
the data would imply positive upper and lower bounds on the new physics
contribution to the weak charge, $\delta_NQ_W$. The required new physics should
be of a type not severely constrained by the high energy precision data. A
simplest possibility would be new neutral vector bosons almost un-mixed to the
$Z$ and with sizeable couplings to fermions. The lower positive bound would
however forbid zero or negative $\delta_NQ_W$ and exclude not only the standard
model but also models with sequential $Z^\prime$, in particular simple-minded
towers of $Z$-like excitations from extra-dimensions. The bound would also
imply an upper limit on the $Z^\prime$ mass within the models allowed.
Conclusions are also derived for models of four-fermion contact interactions.
