  We estimate bubble-nucleation rates for cosmological phase transitions. We
concentrate on the evaluation of the pre-exponential factor, for which we give
approximate analytical expressions. Our approach relies on the use of a real
coarse-grained potential. We show how the coarse-graining scale can be
determined in the studies of high-temperature phase transitions. We discuss the
metastability bound on the Higgs-boson mass and the electroweak phase
transition. We find that the saddle-point approximation is reliable in the
first case and breaks down in the second case.
