  We analyze the power counting of the peripheral singlet partial waves in
nucleon-nucleon scattering. In agreement with conventional wisdom, we find that
pion exchanges are perturbative in the peripheral singlets. We quantify from
the effective field theory perspective the well-known suppression induced by
the centrifugal barrier in the pion-exchange interactions. By exploring
perturbation theory up to fourth order, we find that the one-pion-exchange
potential in these channels is demoted from leading to subleading order by a
given power of the expansion parameter that grows with the orbital angular
momentum. We discuss the implications of these demotions for few-body
calculations: though higher partial waves have been known for a long time to be
irrelevant in these calculations (and are hence ignored), here we explain how
to systematize the procedure in a way that is compatible with the effective
field theory expansion.
