  This paper investigates the importance of radiative corrections for
first-order phase transitions, with particular focus on the bubble-nucleation
rate. All calculations are done with a strict power-counting, and observables
are consistently calculated at every order. This ensures that physical
quantities are gauge and renormalization-scale invariant. Furthermore, to avoid
large logarithms at high-temperatures, an effective three-dimensional theory is
used. This effective theory automatically incorporates higher-order thermal
masses. The results of this paper indicate that sub-leading corrections to the
rate can be large. This is partly because radiative corrections are enhanced
for large bubbles. To illustrate the calculations, three models are considered:
a real-scalar model, a radiative-barrier model, and a model with an effective
dimension $6$ operator. Relevant observables are calculated for each model, and
the reliability of perturbation theory is discussed.
