  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.
