Attempts to apply effective field theory (EFT) methods to nonrelativis
tic nucleon-nucleon (NN) scattering have raised questions about the na
ture and limitations of an EFT expansion when used nonperturbatively.
We discuss the characteristics of a meaningful EFT analysis and compar
e them with traditional approaches to NN scattering. A key feature of
an EFT treatment is a systematic expansion in powers of momentum, whic
h we demonstrate using an error analysis introduced by Lepage. A clear
graphical determination of the radius of convergence for the momentum
expansion is also obtained. We use these techniques to compare cutoff
regularization, two forms of dimensional regularization, and the diba
ryon approach, using a simple model for illustration. The naturalness
of the parameters and predictions for bound-state energies are also sh
own. (C) 1998 Elsevier Science B.V.