There are many controversies over the nonperturbative use of effective field theory (EFT) methods to describe nonrelativistic nucleon-nucleon scattering. I will discuss the characteristics of a meaningful EFT analysis and compare them with traditional phenomenological approaches to nucleon-nucleon scattering. A clear graphical determination of the radius of convergence for the EFT momentum expansion is obtained and used to compare different regularization schemes within a simple model for illustration. The naturalness of the parameters and predictions for other observables such as bound-state energies are discussed.