  We analyse approximate solutions to an exact renormalisation group equation
with particular emphasis on their dependence on the regularisation scheme,
which is kept arbitrary. Physical quantities related to the coarse-grained
potential of scalar QED display universal behaviour for strongly first-order
phase transitions. Only subleading corrections depend on the regularisation
scheme and are suppressed by a sufficiently large UV scale. We calculate the
relevant coarse-graining scale and give a condition for the applicability of
Langer's theory of bubble nucleation.
