The IP method is not tied to any particular set of functions for the inversion basis and each component of the potential can be represented by a different basis. It is an important feature of the IP method, as implemented in IMAGO, that a range of different functions is available, and those which we have applied are specified in [@imago]. Zeroth order Bessel functions and harmonic oscillator functions are both linearly independent sets which have proven useful where bases of large dimensionality are necessary to describe a potential over a wide radial range down to $r=0$. For cases involving light nuclei, particularly for inversion of small $S$-matrix datasets, a small basis comprising a series of Gaussian functions is preferable. A Gaussian basis covering just the nuclear surface region is also useful for heavy ion cases where there is no information available to determine the potential in the nuclear interior. It is important that a basis should not be chosen which would describe the potential over a radial range, or to a degree of detail, which is not warranted by the information contained in the set {$S_l$} or by the nature of the physical situation. In practice, much smaller bases are 