  We discuss contact-interaction searches in the processes e^+e^-\to
\mu^+\mu^-, b\bar{b} and c\bar{c} at an e^+e^- Linear Collider with c.m. energy
\sqrt{s}=0.5 TeV and with longitudinally polarized beams. The measurement of
polarized cross sections allows to study the individual helicity cross
sections, and consequently to derive separate, model-independent, constraints
on the four-fermion contact interaction couplings. We evaluate the reach on
those parameters foreseeable in the case of both electron and positron
polarization fixed at some reference values, and compare it with the situation
where only electron polarization is available. The analysis is based on
polarized integrated cross sections with optimal kinematical cuts that can
improve the sensitivity to the relevant couplings. While electron polarization
would by itself allow such an analysis, the additional positron polarization
(with no loss of beam intensity) and optimization can have a crucial role in
improving the sensitivity to the new interactions.
