We point out a simplicity that arises when we use an interaction in which only an energy with odd $J$ is nonzero. The emphasis is on $J=J_{\text{max}}$ and in particular $J=9^{+}$ in the $g_{9/2}$ shell. It is noted that high overlaps can be deceptive. In many cases a single set of unitary 9-$j$ coefficients gives either an exact or a surprisingly good approximation to the wave function of a nondegenerate state. The many degeneracies that occur in these calculations are discussed and explained. As a counterpoint, we compare the results with an interaction in which both the $J=0$ and $J=J_{\text{max}}$ two-body matrix elements are equal (and attractive). Comparisons with a more realistic interaction are also made.

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