  This paper examines the role that regularization plays in the definition of
the potential used in effective field theory (EFT) treatments of the
nucleon-nucleon interaction. I consider $NN$ scattering in $S$-wave channels at
momenta well below the pion mass. In these channels (quasi-)bound states are
present at energies well below the scale $m_\pi^2/M$ expected from naturalness
arguments. I ask whether, in the presence of such a shallow bound state, there
is a regularization scheme which leads to an EFT potential that is both useful
and systematic. In general, if a low-lying bound state is present then cutoff
regularization leads to an EFT potential which is useful but not systematic,
and dimensional regularization with minimal subtraction leads to one which is
systematic but not useful. The recently-proposed technique of dimensional
regularization with power-law divergence subtraction allows the definition of
an EFT potential which is both useful and systematic.
