In this paper we extend the conventional theory of nucleation to take in the effects of excluded-volume interference between the precritical droplets present prior to phase transformation. It is shown that, close to the critical point, the effect of excluded volume is to cause a sizable increase in the surface free energy of the critical nucleus. A corresponding increase in the barrier to nucleation explains the large undercoolings achieveable experimentally in this region. Our results are compared with recent experimental measurements of Heady and Cahn and favorable agreement is found.