  The nucleation of a lamellar phase from a supercooled homogeneous phase in a
fluctuation driven first-order transition is studied, based on a
phenomenological free energy due to Brazovskii. The absence of phase
coexistence in the corresponding mean-field approximation makes application of
the standard droplet theory of homogeneous nucleation problematic. A
self-consistent coarse-graining procedure is introduced to overcome this
difficulty, and the barrier height for nucleation of a critical droplet is
estimated in the weak-coupling limit. Contrary to earlier estimates the
critical droplet shape is shown to be anisotropic in general. Some effects of
distortions and defects in the lamellar structure are considered and are shown
to affect the critical droplet only very near coexistence where the probability
of nucleation vanishes. The coarse-graining procedure introduced here follows
from a novel application of the momentum-shell renormalization group method to
systems in the Brazovskii class. Possible applications of the theory to the
microphase separation transition in diblock copolymers and to
Rayleigh-B\'{e}nard convection are briefly discussed.
