Are nonrenormalizable theories really unrenormalizable

Using scalar field theories as illustrative models, the paper elaborates on a previous proposal for rendering amplitudes in perturbation theory manifestly finite by expanding in terms of propagators of perturbed dimensions. First phi4 is considered then the scheme is applied to phi6 and, finally, the general case of phisup(n), n(>=)4 and even is discussed. As in the usual approach to perturbation theory, deviations from naive scaling of the amplitudes are observed. But in this scheme, these deviations are due to the nonnaive scaling behaviour of the momentum variables