  Classical nucleation theory has been recently reformulated based on
fluctuating hydrodynamics [J.F. Lutsko and M.A. Dur\'{a}n-Olivencia, J. Chem.
Phys. 138, 244908 (2013)]. The present work extends this effort to the case of
nucleation in confined systems such as small pores and vesicles. The finite
available mass imposes a maximal supercritical cluster size and prohibits
nucleation altogether if the system is too small. We quantity the effect of
system size on the nuceation rate. We also discuss the effect of relaxing the
capillary-model assumption of zero interfacial width resulting in significant
changes in the nucleation barrier and nucleation rate.
