  The subtracted kernel approach is shown to be a powerful method to be
implemented recursively in scattering equations with regular plus point-like
interactions. The advantages of the method allows one to recursively
renormalize the potentials, with higher derivatives of the Dirac-delta,
improving previous results. The applicability of the method is verified in the
calculation of the $^1S_0$ nucleon-nucleon phase-shifts, when considering a
potential with one-pion-exchange plus a contact interaction and its
derivatives. The $^1S_0$ renormalization parameters are fitted to the data. The
method can in principle be extended to any derivative order of the contact
interaction, to higher partial waves and to coupled channels.
