  In standard nucleation theory, the nucleation process is characterized by
computing $\Delta\Omega(V)$, the reversible work required to form a cluster of
volume $V$ of the stable phase inside the metastable mother phase. However,
other quantities besides the volume could play a role in the free energy of
cluster formation, and this will in turn affect the nucleation barrier and the
shape of the nucleus. Here we exploit our recently introduced mesoscopic theory
of nucleation to compute the free energy cost of a nearly-spherical cluster of
volume $V$ and a fluctuating surface area $A$, whereby the maximum of
$\Delta\Omega(V)$ is replaced by a saddle point in $\Delta\Omega(V,A)$.
Compared to the simpler theory based on volume only, the barrier height of
$\Delta\Omega(V,A)$ at the transition state is systematically larger by a few
$k_BT$. More importantly, we show that, depending on the physical situation,
the most probable shape of the nucleus may be highly non spherical, even when
the surface tension and stiffness of the model are isotropic. Interestingly,
these shape fluctuations do not influence or modify the standard Classical
Nucleation Theory manner of extracting the interface tension from the logarithm
of the nucleation rate near coexistence.
