  New observables \sigma_\pm for the process e^+e^-\to\mu^+\mu^- allow one to
get more direct information on additional Z' boson effects than what is
obtained from the canonical ones, \sigma and A_{FB}. Their deviations from the
Standard Model predictions have very specific energy dependences, which are
precisely determined by SM parameters. At energies varying from TRISTAN to
LEP2, one can uniquely predict the signs of \Delta\sigma_{\pm} induced by a Z'
as well as the locations of their extrema and zeros. This unambiguous energy
correlation could be quite useful in distinguishing effects due to Z' exchange
from those caused by other new physics sources. Furthermore, there are two
energy points, \sqrt{s_{+}}\simeq 78 GeV and \sqrt{s_{-}}\simeq 113 GeV, where
the SM quantities \sigma_\pm^{SM} as well as the deviations \Delta\sigma_{\pm}
attain their minimum values or vanish. These points could be very favourable
for a search for new physics beyond the SM and beyond Z' effects.
