  We report analytic solutions of a recently discovered quasi-exactly solvable
model consisting of two electrons, interacting {\em via} a Coulomb potential,
but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere.
Polynomial solutions are found for the ground state, and for some higher
($L\le3$) states. Kato cusp conditions and interdimensional degeneracies are
discussed.
