  In this note we describe the minimal resolution of the ideal $I_f$, the
saturation of the Jacobian ideal of a nearly free plane curve $C:f=0$. In
particular, it follows that this ideal $I_f$ can be generated by at most 4
polynomials. Related general results by Hassanzadeh and Simis on the saturation
of codimension 2 ideals are discussed in detail. Some applications to rational
cuspidal plane curves and to line arrangements are also given.
