Optimal observables for new-physics search at LEP2

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.