Simulations involving the Lennard-Jones potential usually employ a cutoff at r = 2.5σ. This communication investigates the possibility of reducing the cutoff. Two different cutoff implementations are compared, the standard shifted potential cutoff and the less commonly used shifted forces cutoff. The first has correct forces below the cutoff, whereas the shifted forces cutoff modifies Newton's equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted forces cutoff at r = 1.5σ, even though the pair force is here 30 times larger than at r = 2.5σ.