For contact-interaction searches at the Linear Collider, we discuss the
advantages of polarizing both the electron and the positron beams as compared
with polarizing only the electron beam. In particular, for the processes
e^+e^-\to \mu^+\mu^-, \tau^+\tau^-, b\bar{b} and c\bar{c} at a future e^+e^-
collider with \sqrt{s}=0.5 TeV we derive model-independent bounds on the
four-fermion contact interaction parameters from studies of the helicity cross
sections.Comment: 1+15 pages, LaTeX2e, including 7 figure