  One of the most powerful methods for obtaining a precision measurement of M_W
at LEP2 is from direct reconstruction of the invariant mass distribution of W
bosons produced in e+e- --> W+W-. We investigate the effects on the W line
shape, and in particular on the average invariant mass, of phase-space and
first-order Coulomb corrections. The latter are shown to have a non-negligible
effect on the reconstructed mass, inducing shifts of order -20 MeV at collision
energies above threshold, compared to the Born approximation cross section. The
sign and magnitude of the effect can be understood in a simple model
calculation in which one of the W bosons is assumed to be stable.
