  QCD corrections to $e^+e^- \ra WW \ra q_1 \bar q_1 q_2 \bar q_2$ are computed
and presented in a form which allows to impose realistic cuts on the structure
of the observed events. QCD radiation substantially modifies the jet--jet
invariant mass distributions from which the value of the $W$ mass will be
extracted. When the range of allowed jet--jet masses is restricted, as it has
been proposed in order to suppress non--$WW$ backgrounds, the total cross
section is also deeply affected. If all events are forced to four jets,
combining the two partons with smallest invariant mass, and the reconstructed
masses are required to satisfy $ \left| M_{Ri} -M_W \right| \le 10$ GeV $i$=1,2
the lowest order cross section can be reduced by more than 40\%.
