  The fluctuation determinant which determines the preexponential factor of the
transition rate for minimal bubbles is computed for the electroweak theory with
$\sin \Theta_W = 0$. As the basic action we use the three-dimensional
high-temperature action including, besides temperature dependent masses, the $T
\Phi^3$ one-loop contribution which makes the phase transition first order. The
results show that this contribution (which has then to be subtracted from the
exact result) gives the dominant contribution to the one-loop effective action.
The remaining correction is of the order of, but in general larger than the
critical bubble action and suppresses the transition rate. The results for the
Higgs field fluctuations are compared with those of an approximate heat kernel
computation of Kripfganz et al., good agreement is found for small bubbles,
strong deviations for large thin-wall bubbles.
