  The optimal observables with the best ratio of signal to statistical
uncertainty are proposed for a bunch of popular models of the $Z'$ boson. They
are the cross sections integrated over the phase space of the final particles
with proper weight functions. It is shown that the proposed observables are
completely equivalent to the $\chi^2$ fit of the differential cross section, so
they could be used as an alternative of aggregating events into bins with
further minimization of the $\chi^2$ function, especially in preliminary
analysis of experimental data. Application of the observables to the maximum
likelihood estimate of the $Z'$ mass and the $Z$--$Z'$ mixing angle as well as
to the exclusion reach and statistical efficiency of the signal is investigated
in details.
