multi-energy observables for d + alpha scattering. A first report was presented in Ref. [@prl]. The test we now describe is directly relevant and asks the following question: what properties of the potential can reliably be determined from very small sets of $S$?

The test was for deuterons scattering from $^4$He with $S^J_{l'l}$ calculated from a known potential at 11 energies: 8, 8.5 …12.5, 13 MeV. The known potential was energy independent but parity dependent and was taken to be real. (The imaginary parts of empirical potentials are known to be small for d + $^4$He at these energies.) The following terms were included: central Wigner, central Majorana, spin-orbit Wigner and separate even parity and odd parity $T_{\rm R}$ tensor potentials (the odd/even choice for $T_{\rm R}$ reflects what we believe [@prl] to be the case for the actual d + $^4$He tensor force.) The central and spin-orbit terms are like those found in Ref. [@prl], and the very large even parity tensor term is based on that of Dubovichenko [@dubo98], see also [@kuk-new].

The inversion was effectively ‘mixed case’ in the sense just described. The starting potential was zero in all components except for the Wigner real central and 