Testing the efficiency of different improvement programs

We study the finite-size behaviour of a tree-level on-shell improved action for the N -vector model. We present numerical results for N = 3 and analytic results in the large-N limit for the mass gap. We also report a perturbative computation at one loop of the mass gap for states of spatial momentum p. We present a detailed comparison of the behaviour of this action with that of other formulations, including the perfect action, and a critical discussion of the different approaches to the problem of action improvement.