Computer simulation of droplets containingl molecules (l <= 1000) in a lattice gas shows that the average surface area is proportional tol ; 0.6 in two and = 0.825 in three dimensions for small droplets. These exponents agree approximately with those in Kadanoff's modification of Fisher's droplet model near critical points [= (1 + )/; ourT/T c is 0.4, 0.7, and 0.9]. For larger droplets, these exponents change to 1/2 (d = 2) and 2/3 (d = 3), the transition occurring for droplet diameters larger than the coherence length and smaller than the critical diameter in the nucleation of supersaturated vapors. This latter result rises some doubts on a recent nucleation theory of Eggingtonet al.