  The theoretical study of cross sections for polarized--target measurements of
$ \pi N \to \pi \pi N $ reactions gives evidence that the interplay between the
strong contribution from OPE mechanism and the one from isobar exchanges, which
is equally strong within isobar half--widths energy region, must result in
nontrivial polarization phenomena. The Monte--Carlo simulations for asymmetries
in $ \pi^{-} p^{\uparrow} \to \pi^{-} \pi^{+} n $ reaction at $ P_{Lab} = 360
$~MeV/c with the use of theoretical amplitudes found as solutions for
unpolarized data at $ P_{Lab} < 500 $~MeV/c provide confirmations for
significant effect. The effect is capable to discriminate between the OPE and
isobar exchanges and it is sensitive to the OPE parameters in question. This
leads to the conclusion that the decisive $\pi N \to \pi \pi N$ analysis,
aiming at determination of $ \pi \pi $--scattering lengths, must combine both
unpolarized data and polarization information. The appropriate measurements are
shown to be feasible at the already existing CHAOS spectrometer.
