A combination of the aggregation-volume-bias Monte Carlo algorithmand the umbrella sampling technique is applied to investigate homogeneous vapor–liquid nucleation. This combined approach is simple, general, and robust. Its efficiency is demonstrated for nucleationof Lennard-Jonesium, for which the precise calculation of the nucleationbarriers takes only a few minutes at higher supersaturations to a few hours at lower supersaturations. Comparison of the simulation results to the classical nucleation theory (CNT) shows that CNT overestimates the barrier heights by a value nearly independent of the supersaturation, but provides a reasonable description of the critical cluster sizes.