We examine the performance of free-energy perturbation methods when applied to compute the chemical potential of the Lennard-Jones model by Monte Carlo simulation. We emphasize the accuracy and precision of various implementations of the methodology, particularly in the context of the relative effectiveness of ＇insertion＇ vs. ＇deletion＇ approaches. The study is limited to a single state point and system size. In accord with recent arguments made in the context of the hard-sphere model, we find that any single- or multi-stage approach that incorporates a ＇deletion＇ component shows greatly diminished accuracy and precision when compared to its ＇insertion＇ counterpart. We also confirm our earlier conjecture that the entropy rather than the free energy is the important quantity to examine when formulating optimal multistage free-energy perturbation schemes. (C) 1998 Elsevier Science B.V. All rights reserved.