  We apply renormalisation-group methods to two-body scattering by a
combination of known long-range and unknown short-range potentials. We impose a
cut-off in the basis of distorted waves of the long-range potential and
identify possible fixed points of the short-range potential as this cut-off is
lowered to zero. The expansions around these fixed points define the power
countings for the corresponding effective field theories. Expansions around
nontrivial fixed points are shown to correspond to distorted-wave versions of
the effective-range expansion. These methods are applied to scattering in the
presence of Coulomb, Yukawa and repulsive inverse-square potentials.
