We observed nucleation in a first-order phase transition in which a nonequi
librium (metastable) solid phase nucleates and grows from overpressured sup
erfluid He-4 in preference to the equilibrium solid phase. After a time var
ying from a fraction of a second to tens of minutes, the stable phase nucle
ates independently from the liquid, and the nonequilibrium solid phase melt
s. We examined the possibility of accounting for these events in terms of t
he known differences in the interfacial free energies between the superflui
d and the two solid phases (stable and metastable). The experimental result
s are not consistent with this explanation, however, and we discuss other p
ossibilities.