  We investigate the effects of inhomogeneous scalar field configurations on
the electroweak phase transition. For this purpose we calculate the leading
perturbative correction to the wave function correction term $Z(\vph,T)$, i.e.,
the kinetic term in the effective action, for the electroweak Standard Model at
finite temperature and the top quark self--mass. Our finding for the fermionic
contribution to $Z(\vph,T)$ is infra--red finite and disagrees with other
recent results. In general, neither the order of the phase transition nor the
temperature at which it occurs change, once $Z(\vph,T)$ is included. But a
non--vanishing, positive (negative) $Z(\vph,T)$ enhances (decreases) the
critical droplet surface tension and the strength of the phase transition. We
find that in the range of parameter space, which allows for a first--order
phase transition, the wave function correction term is negative --- indicating
a weaker phase transition --- and especially for small field values so large
that perturbation theory becomes unreliable.
